Question

How do you solve: f(x) = -x2e-x
+2xe-x , finding the zero's of f.

Answer 1

0 and 2

Explanation:

`f(x) = -x^2e^(-x)+2xe^(-x)`

To find zeros set f(x)=0 and solve for x

`0 = -x^2e^(-x)+2xe^(-x)`

`0 = -e^(-x)(x^2-2x)`

now factor out x

`0 = -xe^(-x)(x-2)`

set each factor =0 and solve for x

`x=0`

`-e^(-x)=0` no solution for x

`x-2=0, x=2`

zeros of f are 0 and 2