Verify Lagrange's mean value theorem for the function ` f(x) = 2x^(2) -10 x + 29` in the interval [2.7]

Explanation

To verify Lagrange's Mean Value Theorem (LMVT) for the function \( f(x) = 2x^2 - 10x + 29 \) over the interval \([2, 7]\), we will follow these steps:

### Step 1: Check the conditions of LMVT
Lagrange's Mean Value Theorem states that if a function \( f(x) \) 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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