Mean Value Theorem

AP Calculus · Axiom Academy

A powerful theorem connecting average and instantaneous rates of change You drive 120 miles in 2 hours. Your average speed is 60 mph. But at some moment during the trip, were you going exactly 60 mph? The Mean Value Theorem says: YES, guaranteed! In general: if a continuous function connects two points, somewhere in between, the instantaneous rate of change equals the average rate of change. The Mean Value Theorem (Formal) In words: The instantaneous rate of change at point c equals the average rate of change over the interval. Step 1: Find the average rate of change Step 3: Set f'(c) = average rate

This is the written version of the interactive lesson above. See the full AP Calculus course.