need help plz

[placid igloo]

have you learned l'hopital's rule

[merry crest]

hey

yea i believe so

but im struggling

[placid igloo]

ok so what happens if you plug in 3 for x

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x=4

right

[placid igloo]

no x = 3

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oh sorry

3

[placid igloo]

all good lol

so what do you get

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you would get 0 correct?

[placid igloo]

no

whats the top

and whats the bottom

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-12

0

[placid igloo]

how did you get the top as -12

[merry crest]

i did 3 x (-4)

[placid igloo]

the top is f(x) - 4 right?

[merry crest]

yeah

[placid igloo]

x = 3

so its f(3) - 4

theres no multiplication

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oh ok

[placid igloo]

and then whats f(3)

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4

[placid igloo]

ok so what do we get for the top

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not sure

[placid igloo]

we agreed that its f(3) - 4 right

and we just found that f(3) = 4

so can you plug that in

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would it be 0

4-4

[placid igloo]

yep

[merry crest]

ok

[placid igloo]

ok what about the bototm

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i did 3-3

0

[placid igloo]

nice

so we get 0/0

[merry crest]

okay thanks

yea

[placid igloo]

wait were not done

0/0 is indeterminate (as you probably learned in class)

[merry crest]

yeah

so we use the limit process

right

[placid igloo]

mhm

so now what

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do we calculate the rise over run

[placid igloo]

imma be honest i dont know what method your teacher taught you

so idk if i should make you do it how i do it

[merry crest]

lol its okay

you can show me your way if youd like

[placid igloo]

ok sure

[merry crest]

is the answer simple

am i overthinking it?

[placid igloo]

no

[merry crest]

okok

[placid igloo]

so given that if we try and evaluate the limit by plugging in the x = 3, and we get an indeterminate form, l'hopital's rule states that the limit of the quotient is equal to the limit of the quotient of the derivatives

so like $\lim_{x\to 3} \frac{f(x) - 4}{x-3} = \lim_{x\to 3} \frac{\frac{d}{dx}\left(f(x) - 4\right)}{\frac{d}{dx}\left(x-3\right)}$

[wary prawn]

lunaflower

[placid igloo]

do you know how to find the derivative of something

[merry crest]

chain rule

[placid igloo]

that is definitely one way

can you find the derivative of x - 3?

(the d/dx notation means "derivative of")

[merry crest]

1

right

[placid igloo]

yep

can you find the derivative of f(x) - 4 at x = 3

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1

[placid igloo]

close

the derivative means "slope"

can you find the slope of the line at x = 3?

[merry crest]

im not sure

[placid igloo]

here is where rise over run is useful

[merry crest]

so the rise is 5

right

im confused sorry

im messing up

[placid igloo]

all good

lets look at a segment from x=1 to x=4 because that will contain the point that we want (3)

whats the rise for that segment

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3

rught

[placid igloo]

almost

look at f(1) and f(4)

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4

[placid igloo]

for the rise?

[merry crest]

sorry im lost right now

so im looking at f(1) right now and trhe point is on 3

[placid igloo]

yep

and then what about f(4)

the rise is the distance between f(4) and f(1)

[merry crest]

the distance between 4 to 1

[placid igloo]

that would be the run

run is like horizontal movement and rise is vertical movement

notice how from 1 and 4 there are 3 boxes horizontally

[merry crest]

yeah

[placid igloo]

so thats the run

now we need the distance that it travels vertically

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4

[placid igloo]

how did you get that

[merry crest]

5

i just coynted the boxes uo to the rise which would be 5

no?

or is that wrong

[placid igloo]

well we start at f(1)

which is already 3

we want to know how much it increases vertically

[merry crest]

3

[placid igloo]

also sorry about the confusion with the boxes, it shouldnt be boxes, it should be length

[merry crest]

its okay no worries

[placid igloo]

how did you get this

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ohh

6

im so dumb right now

my brain

omg

[placid igloo]

wait still how did you get 6

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i dont know i guessed 6

i really dont know

okay so if f(1) is 3

[placid igloo]

mhm

what is f(4)

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theres no point

would it be 4

since it falls into that line

[placid igloo]

very close, its between 4 and 5

equally

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if it were one to the right

[placid igloo]

so its 4.5

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4.5

[placid igloo]

mhm

[merry crest]

ohh

[placid igloo]

ok so whats the distance

[merry crest]

i was gonna say that but i didnt think thered be a decimal allowed

my apolgies for taking long

3 and 4.5

we add right

so its be 7.5

[placid igloo]

nah we subtract

distance

[merry crest]

1.5

[placid igloo]

if we think about a number line, the distance between 3 and 4.5 is 1.5

yep

so our rise is 1.5

our run is 3

do you know how to get the slope from this

[merry crest]

divided

which gives us 0.5

[placid igloo]

yep

so the slope is 0.5

[merry crest]

okay

phew

[placid igloo]

so whats the final answer

[merry crest]

0.5?

[placid igloo]

yep

gj 🎉

[merry crest]

omg

wow

sorry for taking so much of your time

my brain

thanks for all your help

[placid igloo]

all good lol

[merry crest]

sorry to bother you again but is there any way you can help me out with one more question

i finished all the questions

it sjust this last one

im done

[placid igloo]

sure

[merry crest]

ok thank you

its this

[placid igloo]

ok what do you know about antiderivatives

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a little bit not that much

what do i do here

with all these graphs

[placid igloo]

so an antiderivative is what its name is

the "anti" derivative

so the inverse of a derivative

[merry crest]

oh ok

so in this case

would it be b?

[placid igloo]

why would it be b

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because it starts off by increasing

[placid igloo]

well if f is the anti-derivative of f'

then f' is the derivative of f

so we want to find a graph that we can take the derivative of and get f'

[merry crest]

graph a

has to be

[placid igloo]

why

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it goes down

and then you see goes up again

and increeases up

never mind

if its not a or b

im not sure

do you mind guiding me to the answer please?

[placid igloo]

i have to go 😭

[merry crest]

ah

okay

its fine