calculus

[signal holly]

derivative means slope. First, split the function into 2 functions each for x < 0 , and another for 0 < x. Then compute the derivative and sketch it's graph.

for the case x = 0, the derivative is undefined (there is a hole in the derivative graph at 0)

[misty jungle]

go on

[signal holly]

i think you should know how to compute derivatives, but if you don't know then it is dy / dx = "change in y divided by change in x". Set change in x = 1, which means you take 2 points on the x - axis, which are 1 unit away, Ex : 2 and 3 . Then, compute f(3) - f(2) . This is equal to the derivative of f(x) which are linear. (in this case the functions ARE linear)

[misty jungle]

are u able to like walk me through this question ?

[signal holly]

sure

[misty jungle]

also

like dumb it down

istg calculus is learnign a new language

[signal holly]

what do you mean

[misty jungle]

like

here ill give an example yesterday

it was saying like a whole bunch of giberish

then i asked someone for help

and it basically was asking how many times it crossed the X axis

and i was like oh

😂 put it back in english lmfao

[signal holly]

ok i will try to dumb it down

so this is asking for the slope at each of the points of the function.

slope is rise / run, remember?

[misty jungle]

yeahj

[signal holly]

so calculate that for every point on the graph

ex, try to do (-2, 0). what is the slope at that point?

[misty jungle]

-2,0 to where

[signal holly]

anywhere

[misty jungle]

or are u saying -2 to 0

1/2?

[signal holly]

no i meant the point

[signal holly]

yes

now how about the other points

like (2, -1)

[misty jungle]

1

[signal holly]

nope

[misty jungle]

-1

typo

[signal holly]

yes

great now do that for every point

easy right?

or still need assistance?

[misty jungle]

keep helping lmao

[signal holly]

look at all the points where x < 0

what do you notice about their slopes?

[misty jungle]

all 1

and below it is all 1/2

[signal holly]

?

[misty jungle]

the right side from 0,0 is all -1

the left side is all 1/2

[signal holly]

ok

yes

now plot it

[misty jungle]

like that ?

[signal holly]

yes

but.

how about x = 0?

[misty jungle]

1

[signal holly]

what do you think is the slope?

[misty jungle]

ououou u smart

[signal holly]

no

no

its not 1

and it isnt -1

[misty jungle]

well

[signal holly]

i meant, the slope at x = 0 is UNDEFINED

[misty jungle]

wouldent it share 1/2 and 1 ?

oh

[signal holly]

no.

[misty jungle]

what would make it undefined

[signal holly]

because of this, the logic leads that the slope is undefined

[signal holly]

cause there are 2 possible values for it

[misty jungle]

ahhh

[signal holly]

so draw a hole there ( x = 0 )

to show tthat the slope at x = 0 is undefined

[misty jungle]

so it would be like that ?

[signal holly]

no no

[misty jungle]

oh

[signal holly]

this one, but at (0,1) draw a circle

[misty jungle]

cant

[signal holly]

(0,1) the point, not the interval

[signal holly]

then just submit that

[misty jungle]

this one ?

or with the lines touching 0,0

both

[signal holly]

this one

[misty jungle]

wait i understand this now

[signal holly]

mmost books will draw a circle at (0,1) tho

[signal holly]

great

[misty jungle]

lwk ur good asf at this

by chance

[signal holly]

nah i just went through the course before

[misty jungle]

are u able to help me monday/tuesday to study

[signal holly]

sure

[misty jungle]

alr ill add u

[exotic walrus]

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[misty jungle]

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