A particle is moving along the -axis with a position function . Determine all times when the particle is traveling at its average rate between and seconds.
You are being asked to find all times that the actual velocity is the same as the average velocity on the interval . You are given the position function. How will you find the actual velocity function? How will you find the average velocity on ?
AROC = IROC somewhere
Solve for .
The Mean Value Theorem
The Mean Value Theorem for Integrals
If is continuous on , then there exists at least one point in such that .
The Mean Value Theorem for Derivatives
If is continuous on and differentiable on , then there exists at least one point in such that .