Graphical Differentiation

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Presentation transcript:

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

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

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

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

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

Assignment Lesson 3.5 Page 220 Exercises 1 – 17 odd