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Graphical Differentiation

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Presentation on theme: "Graphical Differentiation"— Presentation transcript:

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) zero slope positive slope zero slope positive slope negative slope

4 Caution When you graph the derivative
You are graphing the slope of the original function Do not confuse slope of original with y-value of 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 the derivative 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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