Find the stationary point and its nature.

Question

To find the stationary point I have to find dy/dx=0

so far I reached until this point where I'm not sure how to get the 2 X values:

dy/dx= how to find the stationary points from here?

Answer 1

$\frac{dy}{dx}=-e^{-x}(x^2+x-2)$

$\frac{dy}{dx}=-e^{-x}(x+2)(x-1)$

Stationary points x=-2 and x=1

L min at x=-2 and L. max at x=1 (first derivative test)