Graphical Differentiation

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
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-value of
  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