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what are 2 things we need to know to define a line?

two points?

slope?

the change in y over the change in x? so the point slope equation?

hmm, im assuming you know what a derivative is for this to work.

yeah but I don't really get derivatives

I know there's 4 types

you should have a simple rule you can apply
constant rule, and a power rule

\[\frac{d}{dx}k=0\]
\[\frac{d}{dx}x^n=n~x^{n-1}\]

I'm just having a hard time applying the equation to these rules

9 - x^2
^ ^
^ this is a power of x
^
and this is a constant

what is the derivative of 9?
what is the derivative of -x^2?

e3rr, -7x^2 ... forgot the equation we were dealing with :/

so for 2 it would be 0 and -7x^2 would be -7x^-6?

how did you get 29?

typo, slip of the fingers.

can you please explain how you got the answer step by step?

your -7x^2 derivative is off ... try it again

sorry my book shows different explanations so I'm a little confused right now

tell me your thoughts then, what does your book explain?

it basically shows me all these rules but all these variables are confusing me

but the examples only show me if I have a point and slope

what is your rule for powers of x?

can you take a picture of it?

For any real number k if y=x^k then d/dx(x^h)= k*x^k-1

let k=2
x^2 become 2x^(2-1)
or simply 2x

so our derivative is
-7x^2 derives to -7(2x), at x=2 that is ... -7(4)

so the 2 becomes x?

out point (2,-26) defines the value of x as 2

*our point ...

2x, when x=2 is just ... 2(2) right?

how did x^2 become 2x?

by the derivative rule you posted. let k=2

x^k derives to k*x^(k-1)

Ohhhh I get it now

but I'm still pretty confused

so now that we know the derivative of -7x^2 to be -7(2x) which is -7(2*2)= -28
what do we do next?

well, thats our slope of our tangent line. the rest is from algebra class.

construct the line using your slope and the stated point

y=mx+b

or point slope equation
y-y1=m(x-x1)

y - f(a) = f'(a) (x-a)
or rewritten as
y = f'(a) (x-a) +f(a)

point slope equation

y-(-26)=-28(x-2)

thatll do it

y=-28x+30

could I get a two out of it to be 2(-14x+15)? or is okay like that?

usually we dont factor it, keep it in y=mx+b form is conventional

okay thank you!!

youre welcome :) and good luck