Unit 5 · Analytical Applications of Differentiation

Chapter 5.2

Where Extremes Live: Critical Points

A maximum can only hide in a short list of places. The Extreme Value Theorem guarantees it exists; critical points say where to look.

10–13 min · free · lesson 24 of 46

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By the end

  1. 01State the Extreme Value Theorem
  2. 02Distinguish local and global extrema
  3. 03Find critical points

In unit 5

  1. 5.1The Mean Value Theorem10–14
  2. 5.2Where Extremes Live: Critical Points10–13
  3. 5.3Finding Extrema with the First Derivative12–16
  4. 5.4Concavity and the Second Derivative Test11–15
  5. 5.5The Complete Portrait: f, f′, f″ Together12–16
  6. 5.6Optimization12–16
  7. 5.7How Implicit Curves Behave10–13
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