Calculus on Demand at Dartmouth College Lecture 19 | Index | Lecture 21
Lecture 20


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In this lecture we learn how to sketch a curve (without graphing calculators) using the first and second derivative.


Quick Question

Which are the graphs of a function, its first derivative, and its second derivative?


Answer

Textbook

Issues in Curve Sketching

Today's Homework

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Quiz

Issues in Curve Sketching Quiz

Examples

  • Consider a continuous function f with the following properties:
    1. f(–2) = 0
    2. f(0) = 1
    3. f(2) = 0
    4. f has a local maximum at x = 0
    Choose a possible graph of f'.
  • Consider a function f which is defined for all real numbers except x = 1, and assume f has a given list of properties. Draw a possible graph of f.
  • Match graphs of three functions with their derivatives.

Applets

  • Curve Sketching: Increasing/Decreasing
  • Curve Sketching: Concavity

Videos

  • click to see the videoDetermine properties of a function from its graph
  • click to see the videoSketch graph of (x – 1)/(x + 1)
  • click to see the videoSketch graph of (x2 – 1)/(x2 + 1)
  • click to see the videoSketch the derivative (1)
  • click to see the videoSketch the derivative (2)

Lecture 19 | Index | Lecture 21