1. Increasing/Decreasing Functions; Average Rate of Change

2. Increasing:____________________
Decreasing: ___________________

3. Mention that “Slope” = “rate of change”.
Slope is constant – 3

4. What is the slope of this graph?
Here “slope” is not constant  “derivative”.
What is the slope of this graph?

5. Average Rate of Change:
On this slide, start off by labeling the endpoints of the secant line as (x1,y1) and (x2,y2). This gives the initial “formula” for A.R.C. Then, erase and label the endpoints as (x1,f(x1)), (x2, f(x2)). This gives the 2nd form for A.R.C. Finally, erase and label the points as (a,f(a)) and (b,f(b)). These points are used in the final formula for the A.R.C. Deriving the A.R.C. formula in this progression makes it easier (I think) for the students to understand where the formula comes from.

6. Have students determine A. R. C. for f(x)=-3x+4 between x=-2 and x=5
Have students determine A.R.C. for f(x)=-3x+4 between x=-2 and x=5. Are they surprised by the answer??