The function `f(x)=x^2\ e^(-x)` is monotonic increasing when (a) `x in R-[0,\ 2]` (b) `0

Explanation

To determine the intervals where the function \( f(x) = x^2 e^{-x} \) is monotonic increasing, we need to follow these steps:

### Step 1: Find the derivative of the function
To find where the function is increasing, we first need to compute the derivative \( f'(x) \).

Using the product rule, we have:
\[
f'(x) = \frac{d}{dx}(x^2) \cdot e^{-x} + x^2 \cdot \frac{d}{dx}(e^{-x})
...