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AP Calculus AB›Unit 5: Analytical Applications of Differentiation›Concavity and graphs

Behavior of Implicit Relations

Implicit differentiation finds where a curve like x² + xy + y² = 7 has horizontal or vertical tangents and how it bends.

Horizontal and vertical tangents
Second derivatives implicitly
Analyzing curves

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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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Accumulation of Change

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Also called: implicit relations, horizontal tangent implicit, vertical tangent