Answer
$y=-3ex-2e$
Work Step by Step
We have: $y(x)=x^2e^{-x}; x=-1$
Now, $y(-1)=[(-1)^2e^{-(-1)}]=e$
We differentiate both sides with respect to $x$.
$y^{\prime}(x)=-x^2 e^{-x} +2x e^{-x}$
The equation of a tangent line at $(-1,e)$ is:
$y-y_1=m(x-x_1)\\ y-e=-3e (x+1) \\ y=-3ex-2e$
