Find the local maximum, the local minimum values, if any, using first or second derivative test of the function f defined by
`f(x)=3x^4-20x^3+36x^2+12`

Explanation

To find the local maximum and minimum values of the function \( f(x) = 3x^4 - 20x^3 + 36x^2 + 12 \), we will use the first and second derivative tests.

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

We differentiate the function \( f(x) \):

\[
f'(x) = \frac{d}{dx}(3x^4) - \frac{d}{dx}(20x^3) + \frac{d}{dx}(36x^2) + \frac{d}{dx}(12)
...