Find the maximum and minimum values of the following functions.
`f(x)=(x^(3))/(3)-(x^(2))/(2)-6x+8`

Explanation

To find the maximum and minimum values of the function \( f(x) = \frac{x^3}{3} - \frac{x^2}{2} - 6x + 8 \), we will follow these steps:

### Step 1: Find the first derivative
We start by differentiating the function with respect to \( x \).

\[ f'(x) = \frac{d}{dx}\left(\frac{x^3}{3}\right) - \frac{d}{dx}\left(\frac{x^2}{2}\right) - \frac{d}{dx}(6x) + \frac{d}{dx}(8) \]
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