Mean Value Theorem Mvt

graph TB MVT(Mean Value Theorem) MVT --> Definition MVT --> Assumptions MVT --> Proof MVT --> Applications Definition --> "If a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one c in the interval (a, b) such that the derivative of f at c is equal to the average rate of change of f over [a, b]" Assumptions --> "Function is continuous on [a, b]" Assumptions --> "Function is differentiable on (a, b)" Proof --> "Use of Rolle's Theorem" Proof --> "Use of Intermediate Value Theorem" Applications --> "Physics: Average velocity" Applications --> "Economics: Marginal analysis"