# differentiable function

#### euclid2

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

#### Chris11

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?

#### skeeter

MHF Helper
suppose that $$\displaystyle f$$ is a differentiable function with the derivative $$\displaystyle f'(x)=(x+1)(x-2)(x+6)$$. 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.

euclid2

#### HallsofIvy

MHF Helper
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!

#### euclid2

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.