Find the local max/min points for the function y=x^2 * e^x

Answer 1

by the product rule

y' = x^2(e^x) + 2x(e^x)
= e^x(x^2 + 2x) = 0 for max/min

e^x = 0 ---> no solution or
x^2 + 2x = 0
x(x+2) = 0
x = 0 or x = -2
if x=0 then y 0
if x = -2 then y = 4(e^2)

so (0,0) and ( -2,4e^2) are max/min points.
I will let you decide which is which.