Unit 5 · Analytical Applications of Differentiation

Chapter 5.7

How Implicit Curves Behave

Back to curves that aren't functions — now with the full toolkit: where they rise, where they bend, where they turn.

10–13 min · free · lesson 29 of 46

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By the end

  1. 01Analyze slopes and tangency of implicit relations
  2. 02Determine where dy/dx or d²y/dx² takes a given sign or value

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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