Find the intervals in which `f(x)=(x^4)/4+2/3x^3-5/2x^2-6x+7` is increasing or decreasing.

Explanation

To determine the intervals where the function \( f(x) = \frac{x^4}{4} + \frac{2}{3}x^3 - \frac{5}{2}x^2 - 6x + 7 \) is increasing or decreasing, we will follow these steps:

### Step 1: Find the derivative \( f'(x) \)
The first step is to differentiate the function \( f(x) \).

\[ f'(x) = \frac{d}{dx}\left(\frac{x^4}{4}\right) + \frac{d}{dx}\left(\frac{2}{3}x^3\right) - \frac{d}{dx}\left(\frac{5}{2}x^2\right) - \frac{d}{dx}(6x) + \frac{d}{dx}(7) \]
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