Answer to Question #282183 in Calculus for bereket

Question

1.     Determine the critical points of each of 

Answer 1

for example:

$f(x) = x^2e^x$

then:

$f'(x) =2xe^x+ x^2e^x=x(2+x)e^x=0$

at critical point $x=0$ :

f'(x) changes its sign from "-" to "+", so this is local minimum

at critical point $x=-2$ :

f'(x) changes its sign from "+" to "-", so this is local maximum