Concavity and Inflection Points
Concavity defined
Inflection points
Example 1: polynomial
Example 2: $f''(c) = 0$ but NOT an inflection point
Example 3: $f''$ DNE at inflection point
Concavity and linearization
Reading concavity from the graph of $f'$
Reading concavity from the graph of $f''$
Example 4: complete concavity analysis
AP exam tips
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Vocabulary
Unit 5 topics
Unit 5 overview15.1 Using the Mean Value Theorem25.2 Extreme Value Theorem and Critical Points35.3 Determining Intervals of Increasing and Decreasing45.4 Using the First Derivative Test55.5 Using the Candidates Test for Absolute Extrema65.6 Determining Concavity and Points of Inflection75.7 Using the Second Derivative Test85.8 Sketching Curves of Functions and Their Derivatives95.9 Connecting f, f', and f''105.10 Solving Optimization Problems