1 / 7

# Graphical Differentiation

Graphical Differentiation. Lesson 3.5. The Derivative As A Graph. Given function f(x) How could we construct f '(x)? Note slope values for various values of x Recall that we said the derivative is also a function. zero slope. zero slope. positive slope. positive slope. negative slope.

Download Presentation

## Graphical Differentiation

An Image/Link below is provided (as is) to download presentation Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

### Presentation Transcript

1. Graphical Differentiation Lesson 3.5

2. The Derivative As A Graph • Given function f(x) • How could we construct f '(x)? • Note slope values for various values of x • Recall that we said the derivative is also a function

3. zero slope zero slope positive slope positive slope negative slope The Derivative As A Graph • Note the graphs of f(x) and f '(x) • Interesting observation • If f(x) is a degree three polynomial ... • What does f '(x) appear to be? f(x) f '(x)

4. Caution • When you graph the derivative • You are graphing the slope ofthe original function • Do not confuse slope of original with y-valueof the original

5. Graphing Derivatives • Original function may have oddities • Points of discontinuity • Not smooth, has corners • Thus the derivative will also have discontinuities • Sketch thederivative of this function

6. Can You Tell Which? • Given graphs of two functions • Which is the original function? • Which is the derivative?

7. Assignment • Lesson 3.5 • Page 220 • Exercises 1 – 17 odd

More Related