Question

Suppose that f(x) = 6x^2 + 3x. Find:

Answer 1

See attachment for full question

Answer 2

What is the question?

Answer 3

I mean, which part don't you get?

Answer 4

how to find the slope at x = 2 and 3.

Answer 5

well, you already got the slope function or derivative on A)
so, use it on B) then :)

Answer 6

oh i plugged it in for f prime (x) and that worked... but the question just says f(x) not prime..

Answer 7

f(x) not prime?

Answer 8

yeah i was plugging it in for the first equation instead of the derivative

Answer 9

oh... k

Answer 10

ok now I don't understand how to do C

Answer 11

for C)
well... first off, find "y", since "x" is given, so you'd have a point (x,y)
keep in mind that "y" is just f(x) so for 2 is f(2) and for 3 is f)3)

then, using the derivative, find the slope at those points
and then plug them all in the point-slope form
that is \(\bf y-f(x_0)=m(x-x_0)\implies y-f(x_0)={\color{brown}{ \frac{dy}{dx}}}(x-x_0)\)

Answer 12

then just solve the point-slope form for "y", to get the tangent's function