# Graphical Differentiation - PowerPoint PPT Presentation

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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.

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Graphical Differentiation

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## 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

### 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)

### 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

### 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

### Can You Tell Which?

• Given graphs of two functions

• Which is the original function?

• Which is the derivative?

### Assignment

• Lesson 3.5

• Page 220

• Exercises 1 – 17 odd