Quote of the Day: 
"A diagram is worth a thousand words." 
   -- Dr. Carl E. Linderholm

Objectives:
   Given the graph of a function, the student will 
determine the graph of the derivative.

1. Collect Homework.

2. Existence of derivatives:
      The derivative does not exist at any of the 
	following:
 

In the examples above, think of derivative as the slope 
     of the curve at a point.  
In the corner or cusp, the slope cannot be equal to two 
     different values at the same point.
In the vertical tangent, the slope cannot be equal to infinity.
In the point of discontinuity, the slope cannot be equal 
     to two different values at the same x-value.

If f(x) is differentiable,
Then it is also continuous.

The converse of this statement is NOT true:
Continuity does not imply differentiability.


3. Graph of the derivative:

    Click here for an interactive link to the Graph of the Derivative

Use tangents to the graph to approximate the slope 
at various points.  Then graph the values of those 
slopes on an axis below the original function.

4. Assignment: 
     p. 187 (15, 23, 24, 25, 26)  

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