Find the points at which the function `f` given by `f(x)=(x-2)^4(x+1)^3` has local maxima and local minima and points of inflexion.

Explanation

To find the points at which the function \( f(x) = (x-2)^4 (x+1)^3 \) has local maxima, local minima, and points of inflection, we will follow these steps:

### Step 1: Find the first derivative \( f'(x) \)

Using the product rule, where \( u = (x-2)^4 \) and \( v = (x+1)^3 \):

\[
f'(x) = u'v + uv'
...