Find the intervals in which the function `f(x)=3/2x^4-4x-45 x+51` is (a) strictly increasing. (b) strictly decreasing.

Explanation

To find the intervals in which the function \( f(x) = \frac{3}{2}x^4 - 4x - 45x + 51 \) is strictly increasing or strictly decreasing, we first need to find the derivative of the function, \( f'(x) \), and then analyze its sign.

### Step 1: Simplify the function
First, we simplify the function:
\[ f(x) = \frac{3}{2}x^4 - 4x - 45x + 51 = \frac{3}{2}x^4 - 49x + 51 \]

...