Calculus Homework + Finding Critical Numbers

Question

f(x)=x²e^6x

 

For this function there are three important intervals: (-∞,A], [A,B], and [B,∞], and [B,∞) where A and B are the critical numbers.

 

Find A: ___

 

and B: ___

Answer 1

f'(x) = 2xe^6x + x²e^6x·6

 

= (2x + 6x²)e^6x

 

= 2x(1+3x)e^6x

 

This is 0 when x = 0 and x = -1/3 so

 

A = -1/3, B = 0