## Definition of *mean value theorem*

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 interval2

**:**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 intervalKeep scrolling for more

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mean value theoremTime Traveler for

mean value theorem## The first known use of

mean value theoremwas in 1900See more words from the same year