Unit 5 · Analytical Applications of Differentiation

Chapter 5.5

The Complete Portrait: f, f′, f″ Together

From a function's derivative alone you can draw its shape blind. The three graphs are one object seen three ways.

12–16 min · free · lesson 27 of 46

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By the end

  1. 01Sketch a function from an analysis of f' and f''
  2. 02Move fluently among the graphs of f, f', and f''
  3. 03Match features across the three representations

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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