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AP Calculus BC›Unit 5: Analytical Applications of Differentiation›Theorems and extrema

Extreme Value Theorem and Critical Points

A continuous function on a closed interval has a max and a min. They happen at critical points, where f′ is zero or undefined, or at the endpoints.

The Extreme Value Theorem
Finding critical points
Local vs. global extrema

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5Analytical Applications of Differentiation

Mean Value Theorem
Extreme Value Theorem and Critical Points
Increasing and Decreasing Intervals
The First Derivative Test
Absolute Extrema: The Candidates Test
Concavity and Inflection Points
The Second Derivative Test
Connecting f, f′, and f″
Optimization
Behavior of Implicit Relations

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Increasing and Decreasing Intervals

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Also called: extreme value theorem, critical points, local and absolute extrema