Question

how would you find f(x) if the derivitive of
f'(x)= (x+1)(x-2)(x+6)?

Answer 1

\[f'(x)= x ^{3}+5x ^{2}-8x-12\] btw

Answer 2

integrate both sides

Answer 3

how do i do that?

Answer 4

\[f(x)=\int x^3+5x^2−8x−12 \ dx\]

Answer 5

also note that \[\int f(x)+g(x)\ dx=\int f(x)dx+\int g(x)dx\]

Answer 6

what does that sign mean?

Answer 7

what course are you taking?

Answer 8

calculus and vectors. The original question states:
Suppose that f is a differentiable function with derivitive f'(x). Find all the critical numbers of f, and determine whether each corresponds to a local max or min, or neither.

Answer 9

You don't need f to do that. You're only interested in how f changes, i.e. in f' (and possibly the derivative of f').

Answer 10

I am assuming that you only need the x-values because that question says critical numbers, not points.

Answer 11

oh okay, well then thats easy