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

## Resources

Math 3 Course Syllabus
Practice Exams

# Contents

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?

### Textbook

Issues in Curve Sketching

### 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

• Determine properties of a function from its graph
• Sketch graph of (x – 1)/(x + 1)
• Sketch graph of (x2 – 1)/(x2 + 1)
• Sketch the derivative (1)
• Sketch the derivative (2)

Lecture 19 | Index | Lecture 21