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
Plot Slope Values with Geogebra

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