mean value theorem

WordReference Random House Unabridged Dictionary of American English © 2025

mean′ val′ue the′orem, [Math.]

1. 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