Please help with finding critical values for the functions.?

Posted on 2017-03-16 18:30:00 in Math by BRIAN

Need help finding critical values for the following functions: 

1.) f(x) = (x^4 / 4) - (x^3 / 3) - 3x^2 + 4 

2.) f(x) = x^2 (3 - x)^2 



This is what I did for the first function (Please correct me for any mistakes): 
f'(x) = 4x^3 - 3x^2 - 6x 
0 = x (4x^2 - 3x - 6) 
I know one of the critical values is x=0. How do I factor out (4x^2 - 3x -6) to find the other critical value(s)? 


Here's what I did for the second function: 
f(x) = x^2 (3 - x)^2 
f(x) = x^2 (3 - x) (3 - x) 
f(x) = x^2 (9 - 3x - 3x + x^2) 
f(x) = 9x^2 - 6x^3 + x^4 
f'(x) = 18x - 18x^2 + 4x^3 
0 = 2x (9 - 9x + 2x^2) 
What do I do after this?...I know one of the critical values is x=0 (from the 2x), but I can't get the other critical value(s) because I'm stuck on how to factor out (9 - 9x + 2x^2).

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