Find all the points of local maxima and minima and the corresponding maximum and minimum values of the function `f(x)=-3/4x^4-8x^3-(45)/2x^2+105` .

Explanation

To find all the points of local maxima and minima and the corresponding maximum and minimum values of the function \( f(x) = -\frac{3}{4}x^4 - 8x^3 - \frac{45}{2}x^2 + 105 \), we will follow these steps:

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

We start by differentiating the function \( f(x) \):

\[
f'(x) = \frac{d}{dx}\left(-\frac{3}{4}x^4 - 8x^3 - \frac{45}{2}x^2 + 105\right)
...