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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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the derivative as a graph
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

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
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
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
Can You Tell Which?
  • Given graphs of two functions
    • Which is the original function?
    • Which is the derivative?
assignment
Assignment
  • Lesson 3.5
  • Page 220
  • Exercises 1 – 17 odd
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