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Mean value theorem

The mean value theorem states, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the connecting line through the endpoints.



Suppose f and g are continous on the closed interval [a, b] and differentiable on the open interval (a, b). Assume further that g ′(x) ≠ 0 for x ∈ (a, b). Then there is a point t ∈ (a, b) such that



The theorem was first proved by the French mathematician Joseph-Louis Lagrange in 1797.

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