Definition Of Mean Value Theorem - Merriam-Webster

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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 See more words from the same year

Rhymes for mean value theorem

• antiserum
• serum
• thiram
• variorum

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mean value mean value theorem mean well See all Nearby Words

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“Mean value theorem.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/mean%20value%20theorem. Accessed 21 Dec. 2025.

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