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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
 Determine properties of a function from its graph
 Sketch graph of (x – 1)/(x + 1)
 Sketch graph of (x^{2} – 1)/(x^{2} + 1)
 Sketch the derivative (1)
 Sketch the derivative (2)
