The interval in which `y = x^(2) e^(-x)` is increasing is:

Explanation

The given function is `y=x^2e^-x`

It will strictly increase in those intervals where `dy/dx>0`

Now,

`dy/dx=-x^2e^-x+e^-x2x`

`impliesdy/dx=e^-x(2x-x^2)`

`e^-x` will be always positive, so the function will strictly increase in those intervals where `2x-x^2>0`

so the function will strictly increase in `(0,2)`