Find all the points of local maxima and local minima as well as the corresponding local maximum and local minimum values for the function `f(x)=(x-1)^3(x+1)^2` .

Explanation

To find the local maxima and minima of the function \( f(x) = (x - 1)^3 (x + 1)^2 \), we will follow these steps:

### Step 1: Differentiate the function
We start by differentiating the function using the product rule.

\[ f'(x) = \frac{d}{dx}[(x - 1)^3] \cdot (x + 1)^2 + (x - 1)^3 \cdot \frac{d}{dx}[(x + 1)^2] \]
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