# mean value theorem

## noun

1
: a theorem in differential calculus: if a function of one variable is continuous on a closed interval and differentiable on the interval minus its endpoints there is at least one point where the derivative of the function is equal to the slope of the line joining the endpoints of the curve representing the function on the interval
2
: a theorem in integral calculus: if a function of one variable is continuous on a closed interval and differentiable on the interval minus its endpoints, there is at least one point in the interval where the product of the value of the function and the length of the interval is equal to the integral of the function over the interval

## Word History

First Known Use

1900, in the meaning defined at sense 1

Time Traveler
The first known use of mean value theorem was in 1900

## Dictionary Entries Near mean value theorem

mean value theorem

## Cite this Entry

“Mean value theorem.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/mean%20value%20theorem. Accessed 28 Sep. 2023.

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