Unit 5 · Analytical Applications of Differentiation

Chapter 5.1

The Mean Value Theorem

If you averaged 60 mph over an hour, at some instant you were doing exactly 60. Obvious-sounding — and one of the most load-bearing facts in calculus.

10–14 min · free · lesson 23 of 46

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By the end

  1. 01Verify hypotheses and apply the Mean Value Theorem
  2. 02Use Rolle's theorem as the special case
  3. 03Draw conclusions about f from facts about f'

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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