Find the extreme points of the following functions. Specify if the extremum is a maximum or minimum. Find the extreme values. `y = xe^(-xcdot), x in (- 2,2)`

Explanation

`y = xe^(-x)cdot x in (-2,2)`
`dy/dx = e^(-x) -xe^(-x)
(d^2y)/dx^2 = - e^(-x) -e^(-x) + xe^(-x) = xe^(-x) -2e^(-x)cdot`
For extremum `dy/dx = 0 rArr x = 1`
`(d^2y)/dx^2]_(x=1) = 1/e - 2/e = 1/e lt 0`
`therefore` Maximum attins at x = 1.
Maximum value =`1/e cdot