Find local maximum and local minimum values of the function f given by`f(x)=3x^4+4x^3-12 x^2+12`.

Explanation

To find the local maximum and local minimum values of the function \( f(x) = 3x^4 + 4x^3 - 12x^2 + 12 \), we will follow these steps:

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

\[ f'(x) = \frac{d}{dx}(3x^4 + 4x^3 - 12x^2 + 12) \]
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