Resources Math 3 Course Home Page Math 3 Course Syllabus Practice Exams Textbook Home Page Post a Comment

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? Answer Textbook Issues in Curve Sketching Today's Homework Log into WebWorK 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