Mean value theorem

In calculus, the mean value theorem states, roughly, that given a section of a smooth curve, there is a point on that section at which the gradient (slope) of the curve is equal to the "average" gradient of the section. It is used to prove theorems that make global conclusions about a function on an interval starting from local hypotheses about derivatives at points of the interval.

Related Topics:
Calculus - Gradient

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This theorem was developed by Lagrange. Some mathematicians consider this theorem to be the most important theorem of calculus (see also: the fundamental theorem of calculus). The theorem is not often used to solve mathematical problems; rather, it is more commonly used to prove other theorems. The mean value theorem can be used to prove Taylor's theorem, of which it is a special case.

Related Topics:
Theorem - Lagrange - Mathematician - Fundamental theorem of calculus - Prove - Taylor's theorem

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