Calc curve sketching

[gray linden]

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[acoustic shale]

can someone please explain how i can sketch it

[torpid quest]

it gives you several points

f(3) = 5, etc.

draw those

[acoustic shale]

yes i did

ty

[torpid quest]

can you show what your progress is

[acoustic shale]

yes

Am I on the right track?

[torpid quest]

it doesn't appear to be decreasing between 3 and 7

[acoustic shale]

is it possible can you show me a quick sketch on how it should look?

[torpid quest]

that would be overhelping

[acoustic shale]

please this is urgent for my tutor 😭

[torpid quest]

but it's convex up when x > 5, and decreasing from 5 to 7

what would look like that

[acoustic shale]

im not to sure

[torpid quest]

what functions can you think of with f'' > 0

[acoustic shale]

parabala?

[torpid quest]

correct

[acoustic shale]

so whens its (3,5) its a parabola?

[torpid quest]

uh, except f''(5) has to be 0

[acoustic shale]

so how would that work

[torpid quest]

i'd try to draw it starting to become more and more linear near 5, i guess

[acoustic shale]

if its possible can i see a quick sketch of it

[torpid quest]

.

[acoustic shale]

please this is really urgent im willing to pay bc i need to hand this in my tutor in 10 minutes 😭

is my first graph correct on the left side?

[torpid quest]

f'(3) should be 0, remember

f'' < 0 for x < 5 should make you think of a downwards-parabola looking thing

[acoustic shale]

ahh

Is it something like this??

[torpid quest]

wat, why'd you move f(3)

f'' < 0 for x < 5

that's the opposite of what you've drawn

[acoustic shale]

so its wrong? i though f'(3) should be 0

[torpid quest]

you're sketching f

not f'

correct?

[acoustic shale]

yes

wait no

[torpid quest]

f(3) can be not 0, even when f'(3) = 0

[acoustic shale]

it says sketch one continuous curve

but i think it implies f(x)

[torpid quest]

yeah it's not clear but we can infer that you are to draw f

[acoustic shale]

yes so

my orginal points were correct?

[torpid quest]

yes

[acoustic shale]

ok so what was wrong with it??

[torpid quest]

but f should be flat when going through (3,5)

you drew it being more sharp

[torpid quest]

and then this

[acoustic shale]

flat?

[torpid quest]

horizontal

at that point

[acoustic shale]

ohh

it passes through flat?

or as a downward parabola

[torpid quest]

well, a downward parabola has a point of flatness

[acoustic shale]

Like this?

[torpid quest]

i think you've tried to draw f'(5) = 0

that's not correct, f'(5) should be less than 0 since 5 is between 3 and 7

instead, f''(5) should be 0

you can interpret that as "not curving there"

kinda linear at that point

[acoustic shale]

please can u help me sketch it

[torpid quest]

i am trying

[acoustic shale]

im sorry im just so confused

is my graph totally wrong?

[torpid quest]

er, kinda

[torpid quest]

this was closer

the biggest problem is that it's not decreasing from 3 to 7

[acoustic shale]

wait what

wdym

[torpid quest]

if you're not very clear on this topic

then maybe it's good if your tutor knows that

[acoustic shale]

yes

but can i just see what it looks like

please this is really urgent like i said 😭

[torpid quest]

well, ask them

[acoustic shale]

i cant this is hw due soon

ill tell them when i hand it in

please man i just really need to see a sketch of it

im desperate please can u just help me 😭 😭 😭

[torpid quest]

i'm trying

i don't think giving you the answer would help

you should understand why your answer is not right

[acoustic shale]

yes but i feel seeing the graph would make more sense to me 😭

[torpid quest]

which is for various reasons depending on which iteration we are talking about

[acoustic shale]

i appreciate your help but can i see what the graph looks like so i can understand better of what youre trying to explain?

[torpid quest]

up until x = 3
down until x = 7
up after

and then the curving is:
say, slope decreasing until x = 5 after which it starts increasing

[acoustic shale]

yes

it increases then goes back down to x=7?

[torpid quest]

yep

[acoustic shale]

isnt that what i did first?|

[torpid quest]

here you can see there's a spot around x = 5.5 in which it is going up

which it is not supposed to

[acoustic shale]

the when does it stop

[torpid quest]

it stops going down at x = 7

that's what f' < 0 for 3 < x < 7 and f' > 0 for x > 7 means

[acoustic shale]

ohh

[torpid quest]

no

the value of the function is supposed, as you move from x = 3 to x = 7, to go only downwards, only decrease, from f(3) to f(7)

you are again drawing f'(5) = 0

which is not one of the requirements

[acoustic shale]

?

[torpid quest]

yeah this is basically right

[acoustic shale]

wait really?

it only decreases?

[torpid quest]

that's what this means

at all points between 3 and 7 it has to be going down

[acoustic shale]

Can u confirm??

[acoustic shale]

ohh but what happened to the downward parabola

[torpid quest]

i think the graph is fine

[torpid quest]

the downward parabola is akin to the part of the graph x < 5

and the upward parabola is akin to x > 5

the places where f'' is supposed to be negative or positive

[acoustic shale]

ohhh ok tysm for the help i think i get it now 😭

wait if f''(x)>0 when x>5

does that mean its decreasing?

[torpid quest]

when f'' > 0, it can be either increasing or decreasing

or flat

f'' is about how the slope is changing, not about the slope

[acoustic shale]

ohhhhhhhhhh

i didnt know that

[torpid quest]

it's like how f' > 0 can allow f to be positive or 0 or negative

[acoustic shale]

yes yes

ok tyhanks again!

[acoustic shale]

hey can u read through my answer and see if its correct?

sorry if my handwriting is atrocious im trying to finish really fast

@torpid quest

[torpid quest]

it's correct

[acoustic shale]

so niko is partially correct

[torpid quest]

your graphs are not right, they're backwards, idk why it even asks you to sketch any graphs at all

[acoustic shale]

he is right about it being a poi but not about a ciritcal point

[torpid quest]

your words are sufficient from my perspective

[acoustic shale]

ah ok ty

my graphs arent correct?

[torpid quest]

yeah

f'' > 0 is like a normal parabola and f'' < 0 is like an upside down parabola

you've drawn it downwards when f'' is +

[acoustic shale]

so it starts off decrreasing?

[torpid quest]

well, as you point out

we can't tell whether f is decreasing or increasing or whatever

since all we have is the f'' information

you can note that f could be increasing all the way, but still look like part of an upside down parabola in one and part of a right side up one in another

[acoustic shale]

yes

so my graph b is wrong?

[torpid quest]

you've drawn the same thing twice and neither is right

[acoustic shale]

so how should i change it

[torpid quest]

well, make it so that f'' < 0 for x > 2 and f'' > 0 for x < 2?

[acoustic shale]

hmm

how does that look like on a graph?

[torpid quest]

.

i don't know what the confusion you're having is

[acoustic shale]

like this?

[jade folio]

Yeah.

That’s how concavity works.