Theorems of Calculus - Theory & Concepts

Understand the foundational theorems that bridge the gap between continuous functions and derivatives: the Extreme Value Theorem, Rolle's Theorem, the Mean Value Theorem, and Cauchy's MVT.

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Mean Value Theorem

There exists at least one point $c$ in $(a, b)$ where the tangent line is parallel to the secant line.

f'(c) = \frac{f(b) - f(a)}{b - a}

Point

c

Secant Slope2.0000

Tangent Slope-1.0000

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Functions, Limits, and Continuity - Theory & Concepts - Limit Explorer Functions, Limits, and Continuity - Theory & Concepts - Epsilon Delta Functions, Limits, and Continuity - Theory & Concepts - Continuity Explorer The Derivative - Theory & Concepts - Secant Tangent

Mean Value Theorem

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