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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 l.jpg

Graphical Differentiation

Lesson 3.5


The derivative as a graph l.jpg

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


The derivative as a graph3 l.jpg

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)


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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


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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


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Can You Tell Which?

  • Given graphs of two functions

    • Which is the original function?

    • Which is the derivative?


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Assignment

  • Lesson 3.5

  • Page 220

  • Exercises 1 – 17 odd


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