Mean Value Theorem Mvt
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"
