I am unable to find values of $x$ for which following function
$x^2 \cdot e^{-x}$
When this function is increasing or decreasing?
My normal approach is "differentiate" but I am stuck at some point...
I am unable to find values of $x$ for which following function
$x^2 \cdot e^{-x}$
When this function is increasing or decreasing?
My normal approach is "differentiate" but I am stuck at some point...
Let $f(x)=x^2e^{-x}$. Differentiate. Using the Product Rule and Chain Rule, we find that $f'(x)=x^2(-e^{-x})+(2x)e^{-x}$, which simplifies to $e^{-x}(2x-x^2)$. But $e^{-x}$ is always positive, and therefore $\dots$.
Not meant to be an answer, but an addendum to André's answer:
Set the derivative $ (2x-x^2)\,e^{-x} > 0 $ to find the region where your function increases. This implies $ x(2-x) > 0 \Rightarrow x>0$ and $(x<2) \Rightarrow x\in(0,2). Try to find the region where your function decreases by setting the derivative of the function less than 0.