help-0

[cunning locust]

😂

[fast lichen]

i def did not

say so

[cunning locust]

you said the sign flips

didnt you

[fast lichen]

i said no such thing

go back and read what i said i cant be bothered

repeating

[cunning locust]

f(-1)>0
f'(-1)>0
f''(-1)<0 ?
smallest in this case would be f''(-1)?

[fast lichen]

why do you think f''(-1)<0?

[cunning locust]

just a guess

[fast lichen]

ok?

why the fuck would you be guessing

all the information is given

[cunning locust]

if something is smaller than 0, then it would be concave up

[fast lichen]

that is not the case

[cunning locust]

but since this isnt a critical point

im lost

[fast lichen]

concave up means you are accelerating positively

f''>0

concave down means you are accelerating negatively (deacceleration)

f''<0

[cunning locust]

ok

so
f(-1)>0
f'(-1)>0
f''(-1)>0

[fast lichen]

ok now why do you think f(-1)>0?

[cunning locust]

because they said

it was increasing

at x=-1

[fast lichen]

well thats why f'(-1)>0

which we already went over

do you even understand what f(x) represents?

think of it like input and output

you put in a value (x)

[cunning locust]

says graph of f increases, f>0

[fast lichen]

can a negative function

not increase?

[cunning locust]

it can increase in a negative direction

[fast lichen]

ok maybe you just dont understand what increase means?

it just means the number gets bigger

-1 is bigger than -5 for example

its not a 'negative increase'

its just called an increase

,w plot 5x

[ocean seal]

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Upgrade to WolframAlpha Pro!

Requested by Køter#5504

[cunning locust]

x<0 is an increase
x>0 increase?

[fast lichen]

for this function it is ALWAYS increasing

the function f(x)=5x i plotted

even when f is negative

you read left to right

[cunning locust]

from -inf to 0, it is decreasing. didnt u say -1 to -5 is increasing

[fast lichen]

you read left to right brother

always

[fast lichen]

-5 to -1

is it clear now what increasing means?

[cunning locust]

oh -1 is bigger . .

[fast lichen]

yes

[cunning locust]

i guess thats true

big -5 is a bigger negative

[fast lichen]

visually it just translates to

the graph going up

when looking from left to right

so the sign of f tells you NOTHING about the sign of f'

[cunning locust]

from left to right it is increasing

at f(x)

because of the concave up

so f(x)>o ?

or f(-1)=0?

[fast lichen]

f(-1)=0. before we move on i think i have to explain

what a function even is to you

[cunning locust]

telepathy incoming

this is whats in my mind ->

[fast lichen]

the line drawn for a function are all possible points satisfying (x,f(x))

you can think of x as the 'input'

and f(x) of the 'output' given you put x in

so the point drawn on your problem

(-1,0)

its on the function curve

so it satisfies (x,f(x))

(-1,f(-1))

f(-1)=0

is that simple

[cunning locust]

-1,0?

[fast lichen]

yes because its on the function line drawn (-1,0) is the same as (-1,f(-1))

because the line itself represents all points in which when you input x you get out f(x)

so you input -1

you get out 0

f(-1)=0

[cunning locust]

oh

f(-1) is the y value

[fast lichen]

sure

[cunning locust]

that doesnt make sense

y value of f(x) is not -1 though, its 0

i think f(-1) is an X VALUE

because you plug in -1 into the x's

[fast lichen]

yes but what you get OUT is f(-1)

after plugging in -1

[cunning locust]

a y value

[fast lichen]

yes as an example lets use f(x)=5x

,w plot 5x

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Køter#5504

[fast lichen]

the line drawn are the points satisfying (x,f(x))

[cunning locust]

ok

[fast lichen]

so lets just come up with a random x value

lets say x=1

f(x)=5x -> f(1)=5 * 1 = 5

[cunning locust]

ye

you got y value

from plugging in that x value

[fast lichen]

the point (1,f(1)) is the point (1,5) on the graph

[cunning locust]

ngl looks like 4.25

but ok

1,5

[fast lichen]

y goes up in 2's

also i just drew it randomly

not very precise

[cunning locust]

your line is perfect

but thats not the issue lol

but i understand

1,5

[fast lichen]

yes so the point (-1,0) on your problem

is (-1,f(-1))

becuase its a point on the function

[cunning locust]

this is like ur saying

[cunning locust]

the point (1,f(1)) is the point (1,5) on the graph

[fast lichen]

yes

[cunning locust]

which is a way

ive never seen anyone do before

like you invented it

[fast lichen]

i def did not

very common in calc

[cunning locust]

no ur right

i remember now

just awk u left it like this

1,f(1)

lol

makes sense now tho

[fast lichen]

good

so just to sum up

f(-1)=0

f'(-1)>0 (increasing)

f''(-1)>0 (concave up)

which is smallest

[cunning locust]

wouldnt this be concave down

f(-1), but y the above^

[fast lichen]

did you undestand why f'?

or just confused about f''

[cunning locust]

ngl im mind blown rn. it said f(x) was increasing

now u be telling me

f(x) = 0

💀

[fast lichen]

no im telling you that the exact input -1 gives you an output of 0

it being increasing would mean that

if you put in a LARGER x

lets say x=0

you would get a LARGER y

[cunning locust]

so what are they on about

if they are saying f(x) >-1

they only give u

one x value

which is x= -1

[fast lichen]

wtf does >-1 mean

[cunning locust]

so techincally

ur staying still

at x=-1

ur not moving

[fast lichen]

thats actually a good point

they are not being 100% accurate

when they say f is increasing on x=-1

that doesnt really make sense

increasing are defined on intervals

so if they say that f is increasing on x=-1 you can think of it like

its increasing in an interval AROUND x=-1

[cunning locust]

well says at x=-1, graph of f increases and is concave up

[fast lichen]

yes read what i said its not very technical way of saying it

[cunning locust]

at x=-1, it is -1. but the graph happens to be increasing

-1 is a point on this increasing graph

which remains still

[cunning locust]

doing so 1sec

[cunning locust]

😮

thats sus man

but sure

ill go with it

every other point

[fast lichen]

well, making infinitesimally small intervals is kind of the whole point of calc no?

[cunning locust]

is increasing

to the left and right of x=-1

sure yea

ok so u cant really

put f(-1)=0, but increasing elsewhere in a notation

💀

[fast lichen]

wdym exactly?

[cunning locust]

i mean this shit is wack

but ill live with it

so which is bigger

in this case

[fast lichen]

they ask for smallest

[cunning locust]

if f' and f'' are increasing

ik

but im asking u now

which is bgger

[fast lichen]

f' and f'' are not increasing remember

they are positive

[cunning locust]

ok

[fast lichen]

f and f' are increaisng

[cunning locust]

f' is

not f

f is at -1

[fast lichen]

what

f(-1)=0 is just ONE point of the function

[cunning locust]

f(-1)=0
f'(-1)>0 (increasing)
f''(-1)>0 (concave up)

[fast lichen]

yes but when i say f

im talking about the function as a whole

[cunning locust]

f in general

[fast lichen]

every point drawn

[cunning locust]

increasing

[fast lichen]

yes exactly

[cunning locust]

i was asking which is biggest at f(-1)

[fast lichen]

the points are going 'up'

[cunning locust]

f' or f''

while you answer that hes another fun one that ima try...

[fast lichen]

i cant tell which is bigger tbh

without being given the explicit form of f

[cunning locust]

f(-1)<0
f'(-1)=0
f''(-1)<0

[fast lichen]

nope

[cunning locust]

f'' is largest

[fast lichen]

you got every single one wrong lol

f(-1) you can tell by looking at the graph

its an exact value remember

input and output

[cunning locust]

f(-1)=0
f'(-1)=0
f''(-1)=0

then

lool

jk

koter it just triggers me man that theyre asking about

f' and f''

when its not even shown

and they dont even give u

[fast lichen]

do one step at a time

[cunning locust]

f'(X) = x^69+420

type of sht

[fast lichen]

its very formulaic

[cunning locust]

there are no steps

[fast lichen]

there is no creative thinking

there isnt even an overlap

in the steps

[cunning locust]

the only steps i need rn is 12

[fast lichen]

every piece of informatuion given

[cunning locust]

jk

[fast lichen]

leads to one equation/inequality

start with determing f(-1)

the information relevant there is the graph given

[cunning locust]

-1,f(-1),

-1,-2

[fast lichen]

yes so what is f(-1)=?

[cunning locust]

f(-1) = -2

[fast lichen]

yup

thats step 1

[cunning locust]

is that less than 0

o.o

[fast lichen]

yes? -2 is less than 0

[cunning locust]

ok so

f(-1) < 0?

😄

[fast lichen]

this gives less information

[cunning locust]

if u say no ima commit murder

[fast lichen]

than f(-1)=-2

its technically right but why would you write it that way lol

[cunning locust]

because its a true statement?

idk

u wanted inequalities

and earlier

u said that f(-1)=0

sooooo... like cmon bruh

[fast lichen]

yes tahts an equality

if you know the EXACT value of something

you use an equality

[cunning locust]

ok so f(-1) < 0, now on to step 2?

[fast lichen]

no

use

f(-1)=-2

why would you ever

[cunning locust]

lol

....

fine

[fast lichen]

change something that portrays more information

into less

[cunning locust]

f(-1)=-2

step2 now?

[fast lichen]

if i tell you i have 5 coins in my hand

and someone asks you

how many coins does that guy have in his hand

if you arent being a complete douche

you would say 5

if you want to be annoying

you say

less than 100

[cunning locust]

D

😆

id point and laugh

and say HAHAHA U HAVE LESS THAN 100, u brokie

[fast lichen]

ok 💀

step 2

f'(-1)

the information relevant now is increasing/decreasing

they tell you its decreasing

[cunning locust]

ok

so

f'(-1)<0

[fast lichen]

yes

step3

the information relevant now is that its concave down

for f''(-1)

[cunning locust]

f''(-1)<0

[fast lichen]

yes

[cunning locust]

we accomplished nothing

all are small numbers

less than 0

[fast lichen]

no wait sorry

i remembered wrong

they tell you its concave up

[cunning locust]

⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️

pog

so smallest

is f(-1)

if the others are f'(-1)>0 and f''(-1)>0

[fast lichen]

f(-1) yes

f(x) you are talking about the function as a whole

[cunning locust]

but they want

the BIGGEST

LARGEST

how do u solve this one koter

🔍

🕵️

[fast lichen]

oh i thouight you were asking me a hypothetical

f'(-1)>0 is not true in our problem

go back to when we did stept2

[cunning locust]

u said

that its concave up

soooooooo

[fast lichen]

yes but remember the relevant information

[cunning locust]

f'(-1) got flipped into >0

[fast lichen]

f(-1) we look at the graph

f'(-1) we see if its increasing/decreasing

[cunning locust]

fuck the graph, we dont have f'(-1) man

[fast lichen]

f''(-1) we see if its concave up/down

they dont interact with eachother

[cunning locust]

around it is decreasing in f(-1)

[fast lichen]

yes

[cunning locust]

f'(-1) would mean increasing

or not idfk

[fast lichen]

stop making

logical conclusions you havent put any thought into

it only serves to confuse you

like saying 'if this about f then this about f' and then this about f'' '

[cunning locust]

u cant "see" anything u can only imagine 😢

[fast lichen]

yes but they tell you so you dont have to see or imagine

just accept 💀

[cunning locust]

u accept something u never seen before

with your own eyes?

⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️ ⁉️

flat earther confirmed?

no way

[fast lichen]

i mean i can also tell its decreasing by looking at graph

but they also tell you so you dont even need to

i think we are getting off track though

[cunning locust]

ok

[fast lichen]

i laid out the plan

[cunning locust]

and true

[fast lichen]

step 1, step 2, step3

[cunning locust]

ok

so which step

are we on now

12th?

accept?

[fast lichen]

no there are only 3 you just forgot the answer to one of them

so do it again

and dont forget

[cunning locust]

its a joke that u prob dont understands its ok tho lol

mb for keeping us off track

ok

step 1 is f(-1)=-2
step 2 is f'(-1)<0 bc the question states f(x) it is decreasing
step 3 is f''(-1)>0 bc the question states f(x) it is concave up

[fast lichen]

i told you dont use = for words

and you put f in every single one

ok for step 2 and 3 put 'because' after and explain

[cunning locust]

should i change the colors too

jk

youre right mb

done

[fast lichen]

step 1 and 2 are correct

step 3 is wrong

sign of f'' is determined by concave up/down

[cunning locust]

its concave up at critical value

were not there tho

[fast lichen]

do you know what concave means

[cunning locust]

is it a cave where conmen stay at after they commit crimes

con-cave

[fast lichen]

concave up is NOT when the function goes up

its a concave shape that points upwards

[cunning locust]

concave up "u"

concave down "n"

[fast lichen]

yes

the point (-1,f(-1)) is still part of the u

even if its on the left side

otherwise you would say concave up would be J

if you are only intersted after the critical point

but its not J its U

[cunning locust]

tbh

concaves do look like J's

sometimes

or most times

because of their inflection points

💀

[fast lichen]

ye maybe not the best way to tell you to consider both sides

since J also has a left side the point could be on

but nevertheless f''(x)>0 at any point on a concave up shape

left or right side

[cunning locust]

kno what i mean dawg

[cunning locust]

really?

[fast lichen]

sure but since they tell you the point is on there

[cunning locust]

even at the maxima?

i find that to be a flaw

[fast lichen]

this might aswell be our point yknow

[cunning locust]

that shit is less than 0 my boy

also they are asking for f''(x)

which we cant see

and would look different

[fast lichen]

you an infer the SIGN of f''(x) by looking at a graph of f

this is what we're doing

[cunning locust]

yes

but at that point is just a point

which falls under the x axis

a negative

however the x value is positive...

i (know) what youre saying

but i dont understand it

f''(x) <0, concave up

and vise versa

[fast lichen]

ok we can work through an example if you want

for some intuition

[cunning locust]

but coudl you maybe graph an example like this

but include f''(x), 3 functions total f - f''

omomgmgg my ocmputer

be bugging?

sec gonna delete an app?

maybe cought a virus or somesht

ok im good now

[fast lichen]

green is f and blue is f''

[cunning locust]

whats f'

sorry go on

[fast lichen]

imagine the function f is a bouncy ball being dropped at some height

so it gets dropped at 9m

at t=0

[cunning locust]

[fast lichen]

and eventually reaches 0m (the ground)

at t=3

then bounces back up again to 9m at t=6

just forget about the physics part of it lol 💀

when you drop it there will be constant acceleration (gravity)

[cunning locust]

but when it reaches 3

it stops

then goes back up at same speed

a reflection

at x=3

and tbh what u described

[fast lichen]

tbh gravity dont really make sense here

[cunning locust]

shoulod look more like a V

than a U

[fast lichen]

anyways

[cunning locust]

explain the constant part

at x=3

or as you would call it t=3

[fast lichen]

but this is the part where infinitesimally small intervals come in

points dont exist in real life

nothing has a velocity at a point

philosophically

calculus goes around that

by not defining velocity and acceleration at points

but at infinitesimally small intervals that we just call points

its the equivalent of taking a picture of a car driving, showing it to you and asking what its velocity is

[cunning locust]

what equation did u graph

i wanna see it on my calc

[fast lichen]

(x-3)^2

[cunning locust]

acceleration stays the same

interesting

legit goes to 0

but ok

i guess it just touches it

very breifly

briefly

[fast lichen]

yes its whole point debacle

have you heard of the rabbit and turtle paradox

[cunning locust]

how come f'(x) is looks like 5x tho?

[fast lichen]

or w.e its called

[cunning locust]

rabbit and turtle?

bro

we gonna get banned

chilll

jk

tell me

about this "rabbit and turtle paradox"

[fast lichen]

oh i think is called zeno's paradox

acchiles and the tortoise

achilles is in a race with the tortoise

he allows the tortoise 100m headstart

[cunning locust]

yes

i head it

i seen it

[fast lichen]

when the turtle is at 100m achilles starts running

[cunning locust]

oh nvm

[fast lichen]

turtle reaches 110m when achilles has reached 100m

bringing their distance closer

they run at constant speeds

which means that when achillies has run 110m

the turtle will have travelled 110m + some extra

and when achillies has then ran that distance the turtle will still be ahead by some

basically stating that by looking at it this way achilles never actually catches up to the turtle

or passes it

[cunning locust]

he techincally

should be able to pass it

after a few seconds lol

but like

[fast lichen]

ofcourse

[cunning locust]

does he have to go at

a set distance

everytime

like 110/10

hes only allowed 80% travel

or something

of the turtle's

[fast lichen]

no but you can imagine that everytime he reaches the turtles previous place

the turtle is still ahead

[cunning locust]

if he walks slow

sure

l0l

wtf

[fast lichen]

no he is faster than the turtle

[cunning locust]

he will pass it then

if hes walking normal

[fast lichen]

realistically yes he will pass it

but how would he pass if it the turtle is always ahead of him

[cunning locust]

if he walks at his normal speed

and does the turtle

human catches up

and passes

zenos

is dumb

and his theroy

theory

[fast lichen]

i think youre missing the point of the paradox

and missing the point of calculus

as a whole as a consequence

[cunning locust]

ye true

taking so long

to learn something so basic

theres another paradox that says if u travel

half the distance

overtime

to a destination

u will never get there

since u reach 0.00000000000000000001

away from

final destination

[fast lichen]

yes its the same idea

[cunning locust]

cool

i get that then

include the turtle

and then im fkd

but yo

if turtle

is also moving

then yes

ok

[fast lichen]

just say the turtle travels half the speed of acchilles

[cunning locust]

its like two of the half distance paradox

i just brought up

but turtle is ahead

so yeah

[fast lichen]

turtle 100m, achilles 0m

[cunning locust]

turtle would always be ahead

[fast lichen]

turtles 150m, achilles 100m

turtle 175m, achilles 150m

[cunning locust]

oh

ok

i gotchu

[fast lichen]

turtle 187.5m, achilles 175m

and so on

[cunning locust]

ye he never reaches

cuz hes got

head start

my boy

[fast lichen]

ye but in an actual race he would obvously pass the turtle

[cunning locust]

he wont have turtle soup

after all

[fast lichen]

which is the whole paradox thing

[cunning locust]

yeee

understood

now why did u show me this

the f''(x) is always constant

bcuz of this theroy ?

at x=3 its too small

of a number

therefore doesnt change

?

[fast lichen]

looking at single points brings forward things that dont seem to be true

because single points dont exist in real life

really

[alpine sable]

||(Can any1 of you come #help-2 when you are done?? I need a help on single equation and rest of the work is done, Thank you)||

[fast lichen]

so its no that there exists a point x=3 where the acceleration exists

think of it as an infinitely small interval and it makes perfectly sense

idk if im explaining it well

[cunning locust]

idk just trying to understand y f''(x) is constant

but i think i get it

bcuz its always moving

even at x=3

now f' on the other hand

not too sure

can u add 2(x-3)

into your graph

[fast lichen]

the f' is always moving which is why

f is stopped though at x=3 exactly

[cunning locust]

so then

it wouldnt be moving

at x=3

for f(x)?

but for f'(x) it is?

[cunning locust]

ty

its decreasing from (-inf, 3) for f and f'.
increasing from (3,inf) for f and f'.
constant at f''(x)

is this correct?

[fast lichen]

close

f' is always increasing

the red line is always going up

also f is decreasing in (-inf,3] and increasing in [3,inf)

[cunning locust]

the picture proves against this?

[fast lichen]

is -2 not defined in the function?

[cunning locust]

its defined

i think that f'(X) is always increasing

but if u look at it specifically

at certain points

it changes

if u look at x=-5

its gonna be decreasing

but yes you are right the function as a whole is increasing

i think?

this is the type of shit koter

that confuses me

like

ik if u lok at that graph

oh

ez

its increasing

but here

in that phot i just sent u

it says

decreases

and increasings

[fast lichen]

oh did you send me a graph of f'?

[cunning locust]

💀

ye

[fast lichen]

well thats why then

they are asking you if f is increasing/decreasing

based on a graph of f'

[fast lichen]

we can also do the same with our example

[cunning locust]

you said this.

which is false?

[fast lichen]

you are not properly distinguishing between f and f'

i said f' is increasing

the question is asking you about f

FROM a graph of f'

[cunning locust]

that is given,

which is displayed there

[fast lichen]

f' is shown not f

[cunning locust]

oh they did say

sketch

graph of f

well

thats later

actually

thats what remains

[cunning locust]

how would u even be able to tell if there is no maximum? bc the x value on this graph f'(x) is touching the negative side and is increasing?

[fast lichen]

this is our (x-3)^2 example btw

[fast lichen]

because f' is decreasing then increasing

actually its the same as our example

it decreases then increases

no maxima

[cunning locust]

so lets add

f''

its always moving

and is positive

tehcnically

[fast lichen]

'moving' in what sense

[cunning locust]

all of these are always moving

graph wise idk

left to right

[fast lichen]

you would usually say its constant

because its not moving

[cunning locust]

oh

[fast lichen]

doesnt go up or down

f''(x)=2

[cunning locust]

so it remains

speed

of 2

[fast lichen]

what speed are you talking about

[cunning locust]

acceleration of 2

i mean

[fast lichen]

yes

[cunning locust]

how can u be accelerating

at a constant speed

0l

l0l

[fast lichen]

well velocity is not constant

its always increasing

[cunning locust]

yes

but

f'' is constant

acceleration

and im asking how can it be constant

that would just mean ur traveling at a steady speed

or ur constantly

increasing ur speed

[fast lichen]

no constantly accelerating means you go faster and faster

[cunning locust]

which i think is true?

[fast lichen]

yes

[cunning locust]

at a rate of 2?

[fast lichen]

yes you increase your speed by a rate of 2

[cunning locust]

all the way from the negatives

to the positives

of f'

[fast lichen]

yes

[cunning locust]

and f i guess

interesting

ok

now

let me ask u

which is bigger

[cunning locust]

at x=3.5?

of f, f', and f''

[fast lichen]

well i know the explicit form of the function

(x-3)^2

so its just plugging in values

f(3.5)=1/4

f'(3.5)=1

f''(3.5)=2

[cunning locust]

ok which is smaller

also

cant u just look at graph

and tell me

f, f', and f''

at x=3.5

[fast lichen]

you have to make some educated guesses then if you are just looking

[cunning locust]

i realize u can plug in

but for the sake of our anoyying as problem we had

earlier

without being told

whats what

u feel me

we were only given

f

[fast lichen]

but from our problem we had f(-1)=-2, f'(-1)>0 and f''(-1)>0

so f(-1) is obviouslyt smallest

if you cant do this you really just have to guess

i mean i can from our example see that f(3.5) is def smaller than f'(3.5)

but between f(3.5) and f''(3.5) i wouldnt really know

[cunning locust]

f is smaller than f', f' is smaller than f''

f<f'<f''

at x=3.5

[fast lichen]

i guess just make rough approximations

you know f(3.5)=1/4

then look at rise/run for 3.5 and 4 for example

then look at rise/run for 4 and 4.5 for comparison to see acceleration

[fast lichen]

oh you mean if everyyhing is drawn

[cunning locust]

ignore the green

i messedup

[fast lichen]

i thought you means just from f

[cunning locust]

1 goes a bit higher

[fast lichen]

yes i understand

i just thought you meant finding out from this

[cunning locust]

well

[fast lichen]

this is perfectly fine

[cunning locust]

couldnt se oit

ew do it

lets say

-2.5

x=-2.5

now we know its decreasing there

and its concave up

so lets do

the 3 steps

[fast lichen]

sure its x=2.5 btw

there will still be some approximative guess work at the end but i will get to that

[cunning locust]

f(2.5)>0 bc it's y value is greater than 0, above the x axis
f'(2.5)<0 bc graph says f(x) is decreasing
f''(2.5)>0 bc graph is in 2nd quadrant and upward concave?

[fast lichen]

yep so do the 3 steps

[cunning locust]

how does that look

oh yeah

assume we dont have

the function

only graph

[fast lichen]

looks ok but 2nd quadrant doesnt matter for f''

only concave up/down

[cunning locust]

noted

[fast lichen]

and you want to figure out what is largest?

[cunning locust]

sure

[fast lichen]

then do some approximations for f(2.5) and f''(2.5)

[cunning locust]

f' or f''

[fast lichen]

since those are the ones you are considering

[cunning locust]

how would one find out

f''(2.5) without

function

y''=mx+b w.e.

ok fk it koter

we established

f' is smallest

and f and f'' is bigger

lets move on

heres one

ima try to solve

f(-2)=3 bc thats the value mofo
f'(-2)<0 bc says f(-2) is decreasing
f''(-2)>0 bc concave up

smallest? f'(-2)

is this correct? @fast lichen

[fast lichen]

yes

[cunning locust]

finally

i understood this

[cunning locust]

sht

[fast lichen]

this is one way to approximate acceleration

you do rise/run from 2 points

and see how much that changed between them

[cunning locust]

f'' u wouldnt be able to find tho right?

or could u

[fast lichen]

remember f'' is change in slope

so if we have 2 f' values

[cunning locust]

change of slope is 1/2?

thats f'

not f''

[fast lichen]

no slope of secant is -1/2 then 1/2

then we use those 2 values

to find f''

the slope changed by 1

from -1/2 to 1/2

[cunning locust]

slope changed by 1?

ok

interesting

[fast lichen]

and it took a distance of 1/2

so 1/(1/2)=2

acceleration is 2

[cunning locust]

but its 2 tho, not 1

[cunning locust]

wym

[fast lichen]

actually its not clear whether you would use 1 or 2

so just use 1.5

as an approximation

[cunning locust]

f'' = 1/difference of slopes?

[fast lichen]

and 1.5>1/4 so f'' is largest

f''=difference of slopes/distances between slopes

but distance between slopes is kind of a weird metric

cause are you tkaing distance between boints x=2.5 and x=3.5

or x=2.5 and 3

[cunning locust]

starting at which points? from far ends? or close by

[fast lichen]

exactly its not clear so just choose something

its supposed to be an approximation anyways

like an eyeball test

[cunning locust]

so between 1 slope

so half of a half

1/4

so, 1/(1/4)?

=4

[fast lichen]

i think 1/4 is not realistic

either 1/2 or 1

or somewhere inbetween

[cunning locust]

maybe its this modified: f''=difference of slopes/distance of a slope

but tbh, in our example

from mymathlab

[fast lichen]

well is like 2 approximations in 1

[cunning locust]

it doesnt show u critical value

so ur kinda fucekd

lol

[fast lichen]

critical value is not relevant

[cunning locust]

o.o

[fast lichen]

just choose 3 points on the curve

[cunning locust]

i guess

[fast lichen]

i think you can use either one of those distances

[cunning locust]

1/1/2

seems promising

[fast lichen]

1/2 gives us our correct one though

ye

[cunning locust]

so like, ud do the same here?

ud pick 3 points

equal distance tho

(-5,4),(-2,-3),(1,2.5)

then do rise over run

for both sides

then ud do

6/(slope)

6/(-1/3)

and ud get -18

for the y''?

f''= (-1,18)?

[fast lichen]

no also f''=(-1,18) makes no sense notation wise

a function of 1 variable cant be equal to a point

[cunning locust]

f''(-1) = 18

better?

[fast lichen]

your rise/run for the first two points are

[cunning locust]

🔸 🔸 🔸 🔸

thought u wanted f''=difference of slopes/distance of a slope

is difference not the x values

from -5 to 1? which is 6

like u did earlier

[cunning locust]

here, the red

1/ (1/2)

[fast lichen]

i think you forgot how we got 1?

[cunning locust]

its 1

yes

[cunning locust]

but here in our fresh example we got 6

[fast lichen]

1/2-(-1/2)=1

thats how we got 1

we found the difference of the two rise/run values

[cunning locust]

2.5 - 3. is .5. 3 to 3.5 is .5

.5+.5=1

[fast lichen]

that is not what we did

[cunning locust]

if we add the slopes we get 6?

[cunning locust]

oh

[fast lichen]

you take the DIFFERENCE of slopes

aka how much it changed

cause that is what acceleration measures

how much slope changes

[cunning locust]

-1/3 to -1/3

0?

o.o

looool

stays the same

[fast lichen]

it does not

first slope is -1/3

2nd slope is -0.5/3

run is 3 in both

[cunning locust]

not -.25/3?

[fast lichen]

but it goes from 4 to 3 in the 1st two points

[cunning locust]

oh nvm

.5

mb

[fast lichen]

and 3 to 2.5

[cunning locust]

so the differnce

is -.5?

6/.5?

is our answer?

for f''(-2)?

[fast lichen]

what is the difference between -2/6 and -1/6 (the 2 slopes)

i feel like you are flying through the algebra without thinking about it

[cunning locust]

why u doing -2/6 brah

and -1/6

whats ur formula

f''=difference of slopes/distances between slopes?

.5/6?

[fast lichen]

-1/3 and -0.5/3 -> -2/6 and -1/6

im removing the decimal

and putting common deniominator

so its easier to compare

because you apparently think the difference is 0.5

because you dont want to actually think and do the algebra

but just see 2 numbers

and say something

[cunning locust]

-.5

differnece

[cunning locust]

here

[fast lichen]

idk my patience is running thin

[cunning locust]

l0l

[fast lichen]

we are regressing

[cunning locust]

i tried

[fast lichen]

into fractions

[cunning locust]

to plug into calculator

(-2/6)+(-1/6)

[fast lichen]

i already had to explain functions to you which should be mastered when starting calc

but i cant start to explain fractions to you

this is khan academy job

sorry

[cunning locust]

difference

is minus

mb

just trying to know

if im subtracting

from -2/6

first

or -1/6 first

thats the issue

i can do fractions bro

trust me

like if u were to ask subtract 1 from .3

answer would be -.7