Find the interval of monotonocity of the function `f(x)=|x-1|x^2dot`

Explanation

To find the intervals of monotonicity of the function \( f(x) = |x - 1| x^2 \), we will follow these steps:

### Step 1: Define the function based on the absolute value
The function \( f(x) = |x - 1| x^2 \) can be split into two cases based on the value of \( x \):

1. **Case 1**: When \( x \geq 1 \), \( |x - 1| = x - 1 \)
\[
f(x) = (x - 1)x^2 = x^3 - x^2
...