Verify Lagranges mean value theorem for `f(x)=x(x-2)` on `[1,\ 3]` on the indicated intervals. Also, find a point `c` in the indicated interval:

Explanation

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

### Step 1: Check Continuity and Differentiability
Lagrange's 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 point \( c \) in \((a, b)\) such that:

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