mean value theorem

Also known as Lagrange's mean value theorem, mean value theorems, law of the mean, MVT

on the existence of a tangent to an arc parallel to the line through its endpoints

AI overview

The mean value theorem states that for any smooth curve between two points, there must be at least one spot on that curve where the tangent line is parallel to the straight line connecting the endpoints. This matters because it's a fundamental tool in mathematics that helps us understand how functions behave and is essential for proving many other important results in calculus.

AI-generated from the Wikipedia summary — may contain errors.