Real Analysis (Advanced Calculus) Archives - Page 2 of 2 - Infinity is Really Big

January 15, 2019July 13, 2019

Deconstructing the Mean Value Theorem, Part 2

The Mean Value Theorem says there’s at least one point where the slope of the tangent line on a smooth curve equals the slope of the secant line between the endpoints.

At its heart, the Mean Value Theorem is fairly intuitive. It essentially states that a smooth curve has at least one tangent line whose slope is equal to the

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January 8, 2019July 13, 2019

Deconstructing the Mean Value Theorem, Part 1

Visual interpretation of the Mean Value Theorem. — The Mean Value Theorem says there’s at least one point where the slope of the tangent line on a smooth curve equals the slope of the secant line between the endpoints.

Many mathematicians start chanting “MVT! MVT! MVT!” when they see the Mean Value Theorem in action. This is indeed because it is so valuable.

What does it mean … Read the rest