1. ## differentiable function

suppose that $f$ is a differentiable function with the derivative $f'(x)=(x+1)(x-2)(x+6)$. find all the critical numbers of f and determine whether each corresponds to a local maximum, a local minimum, or neither.

2. Use the first derivitive test...

When is f'(x)=0? What are the signs of f'(x) in the intervals between these points, and beyond them?

3. Originally Posted by euclid2
suppose that $f$ is a differentiable function with the derivative $f'(x)=(x+1)(x-2)(x+6)$. find all the critical numbers of f and determine whether each corresponds to a local maximum, a local minimum, or neither.
critical values occur where f'(x) = 0

local maximums occur at critical values where f'(x) changes sign from positive to negative.

local minimums occur at critical values where f'(x) changes sign from negative to positive.

4. Euclid2, you have posted 4 questions, of the same kind, in a row where you have not shown any attempt to do them yourself. This is not a "we will do your homework for you" forum!

5. Originally Posted by HallsofIvy
Euclid2, you have posted 4 questions, of the same kind, in a row where you have not shown any attempt to do them yourself. This is not a "we will do your homework for you" forum!
nothing of the sort. i had 17 homework questions last night. i was unable to do 5 of them. i posted them here.