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Graphical Differentiation

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Graphical Differentiation

Lesson 3.5

- 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

- 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)

- When you graph the derivative
- You are graphing the slope ofthe original function
- Do not confuse slope of original with y-valueof the original

- Original function may have oddities
- Points of discontinuity
- Not smooth, has corners

- Thus the derivative will also have discontinuities
- Sketch thederivative of this function

- Given graphs of two functions
- Which is the original function?
- Which is the derivative?

- Lesson 3.5
- Page 220
- Exercises 1 – 17 odd