<Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> <P> In mathematics, the mean value theorem states, roughly, 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 secant through its endpoints . </P> <P> This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval . </P> <P> More precisely, if a function f (\ displaystyle f) is continuous on the closed interval (a, b) (\ displaystyle (a, b)), and differentiable on the open interval (a, b) (\ displaystyle (a, b)), then there exists a point c (\ displaystyle c) in (a, b) (\ displaystyle (a, b)) such that: </P>

Mean value theorem for functions of several variables
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