Critical Points?

Question

Consider the function f(x) = X^2e^3x

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

What are A and B?

Answer 1

I'm not going to calculate this now but the intervals could differ in sign of derivative (increasing or decreasing function) or curvature (double derivative, increasing or decreasing derivative function).

Answer 2

I suppose you call critical points those with derivative = 0

f´(x) = 2x*e^3x +3x^2 e^3x = e^3x( 3x^2 +2x)

f´(x) = 0 x= 0 and x= -2/3 A =-2/3 B=0