Verify Mean Value Theorem, if `f(x)=x^3-5x^2-3x` in the interval [a, b], where `a = 1 and b = 3`. Find all `c in (1, 3)` for which `f^(prime)(c)=0`.

Explanation

To verify the Mean Value Theorem (MVT) for the function \( f(x) = x^3 - 5x^2 - 3x \) on the interval \([1, 3]\), we will follow these steps:

### Step 1: Check the conditions of the Mean Value Theorem
The Mean Value Theorem states that if a function is continuous on the closed interval \([a, b]\) and differentiable on the open interval \((a, b)\), then there exists at least one \( c \) in \((a, b)\) such that:

\[ f'(c) = \frac{f(b) - f(a)}{b - a} \]
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