Find the absolute extrema of

Question

f(x)= (2x-1)e^(-x) on [0, 00)

Answer 1

f ' (x) = (2x-1) e^(-x) ( -1) + 2 e^(-x)
= 0 for a max/min

e^(-x) (2 - (2x-1)) = 0
e^(-x) ( 3 - 2x) = 0
e^(-x) = 0 ----> no solution
or
3 - 2x = 0
x = 3/2
then f(3/2) = 2e^(-3/2) = 2/e^(3/2)