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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.

##### Explanation

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

## HistoryThe theorem was first proved by the French mathematician Joseph-Louis Lagrange in 1797. |