The First Derivative Test
The test
Why it works
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Example 1: two local extrema
Example 2: critical point that is not an extremum
Example 3: $f'$ DNE at critical point
Example 4: rational function
Using the first derivative test with graphs
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Justification template for AP FRQs
First Derivative Test vs other tests
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