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Graphical Differentiation

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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  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. 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)

  4. 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

  5. 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

  6. Can You Tell Which? • Given graphs of two functions • Which is the original function? • Which is the derivative?

  7. Assignment • Lesson 3.5 • Page 220 • Exercises 1 – 17 odd

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