Critical Numbers

Calc12

New member
Joined
Nov 17, 2010
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39
Hello,

I am trying to find the critical numbers for

f'(x) = 36x^3 - 72x^2 - 72

I got it to:
36(x^3 - 2x^2 - 2)

However, I am confused to as if I am supposed to factor it more? If so how would I factor it further?
Or how would I solve for
36(x^3 - 2x^2 - 2) = 0

Thanks very much in advance.
 
Calc12,

 1)  Work out f(x).  Youll get a quadratic.  There will be no nonzero constant\displaystyle \ 1) \ \ Work \ out \ f'(x). \ \ You'll \ get \ a \ quadratic. \ \ There \ will \ be \ no \ nonzero \ constant

 after that step. (In this case it will be equal to 0).\displaystyle \ after \ that \ step. \ (In \ this \ case \ it \ will \ be \ equal \ to \ 0).


 2)  Set this derivative equal to 0 and solve for the critical numbers.\displaystyle \ 2) \ \ Set \ this \ derivative \ equal \ to \ 0 \ and \ solve \ for \ the \ critical \ numbers.

a)  Factor out the greatest common factor.\displaystyle a) \ \ Factor \ out \ the \ greatest \ common \ factor.

b)  Set each factor (monomial or binomial) equal to 0 and solve for the real  xvalues\displaystyle b) \ \ Set \ each \ factor \ (monomial \ or \ binomial) \ equal \ to \ 0 \ and \ solve \ for \ the \ real \ \ x-values

(critical numbers.)\displaystyle (critical \ numbers.)
 
Thanks so much for your time.

However, it seems like I added wrong in the first derivate test :| drove me crazy and I figured it out :)
I appreciate your help!!
 
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