It just so happens that Hustling Harry’s grade in math class at any week during the semester is calculated by . At what point during the ‑week semester is Harry’s grade equal to his average grade for the semester?
This is an application of the Mean Value Theorem.
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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 .