Word Count : 318

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To apply Lagrange's Mean Value Theorem (MVT), we first recall that the theorem states that for a function \( f \) that is continuous on the closed interval \([a, b]\) and differentiable on the open interval \((a, b)\), there exists at least one point \( c \) in the interval \((a, b)\) such that: \[ f'(c) = \frac{f(b) - f(a)}{b - a} \] We are given the function \( f(x) = 2x^2 - 7x - 10 \) over the __________ ______ ________ ______ ____ ___ ________ _______ _________.
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