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
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Math.
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. Also called law of the mean, theorem of the mean.
[1900-05]
Useful english dictionary. 2012.