# mean value theorem

- the theorem that for a function continuous on a closed interval and differentiable on the corresponding open interval, there is a point in the interval such that the difference in functional values at the endpoints is equal to the derivative evaluated at the particular point and multiplied by the difference in the endpoints.

## Origin of mean value theorem^{}

First recorded in 1900–05

Also called law of the mean, theorem of the mean.

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018