The Mean Value Theorem
Statement of the MVT
Geometric meaning
Why the hypotheses matter
Example 1: finding $c$
Example 2: trig function
Rolle's Theorem (special case)
MVT applied to data tables
MVT for proving inequalities
AP exam applications
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MVT vs IVT comparison
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