differentiable function

May 2008
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Ottawa, Canada
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.
 
Sep 2009
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18
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
Jun 2008
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North Texas
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.
 
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HallsofIvy

MHF Helper
Apr 2005
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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!
 
May 2008
400
82
Ottawa, Canada
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.