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What is Rolle's Theorem and the Lagrange Mean Value Theorem (LMVT)?

Study flashcard from the deck JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry.

Answer

LMVT states that if $f$ is continuous on $[a, b]$ and differentiable on $(a, b)$, there exists $c \in (a, b)$ such that $f'(c) = \frac{f(b) - f(a)}{b - a}$.

Explanation

Rolle's theorem is the special case where $f(a) = f(b)$, guaranteeing at least one stationary point where $f'(c) = 0$.

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