Find the intervals of monotonicity of the following functions.
`(i) f(x) =x^(2) (x-2)^(2) (ii) f(x) =x ln x`

Explanation

To find the intervals of monotonicity for the given functions, we will follow these steps:

### (i) For the function \( f(x) = x^2 (x-2)^2 \)

1. **Find the derivative \( f'(x) \)**:
We will use the product rule. Let \( u = x^2 \) and \( v = (x-2)^2 \).
\[
f'(x) = u'v + uv'
...