Find the intervals in which the function f given by `f(x)=4x^3-6x^2-72 x+30`is (a) strictly increasing (b) strictly decreasing

Explanation

To find the intervals in which the function \( f(x) = 4x^3 - 6x^2 - 72x + 30 \) is strictly increasing and strictly decreasing, we will follow these steps:

### Step 1: Find the first derivative \( f'(x) \)
To determine where the function is increasing or decreasing, we first need to find the derivative of the function.

\[ f'(x) = \frac{d}{dx}(4x^3 - 6x^2 - 72x + 30) \]
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