Question

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

Answer 1

Answer:

0 and 2

Step-by-step 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