Graphical Differentiation

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# Graphical Differentiation - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Graphical Differentiation' - parry

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Presentation Transcript

### 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