3.5 Issues in Curve Sketching



The first and second derivatives are used to sketch a curve by hand. Hence, f' and f'' are being used to get graphical information about f. For example, where is f increasing or decreasing, and where does it have local maxima or minima?

By the end of your studying, you should know:

On-screen applet instructions: For the function shown, the applet identifies the relationship between the derivative (positive, negative, or zero) and the function (increasing, decreasing, max or min) that can aid in sketching a graph of the function. Use the slider to move the point P along the curve.


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.


Curve Sketching: Increasing/Decreasing
Curve Sketching: Concavity


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See Exercises for 3.5 Issues in Curve Sketching (PDF).

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3.4 Slope Fields and Euler?s Method Table of Contents 3.6 Optimization

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel