1. Average Rates of Change
By the end of today’s class, I will be able to:
 calculate the Slope of a Secant for any polynomial function
 understand that A.R.C. (Average Rate of Change) gives a rate that approximately describes the graph as “generally increasing” or “generally decreasing” for a specified interval

2. Average Rates of Change
Given a function, y = f(x), the Average RoC (“Rate of Change”)
of y with respect to x, over an interval from x1 to x2 is given by the Slope of the Secant through (x1, y1) and (x2, y2)
<< A secant is a line that has 2 points of intersection with the curve. >>
A.R.C. = =

3. Average Rates of Change
Given:
(-2,14)
A.R.C. = =
(4,-4)
Therefore between x=-2 and x=4, the y-coordinate is decreasing at an average rate of 3 units/unit!

4. Average Rates of Change
For Non-Linear Functions:
- R.o.C. varies depending on the location on the curve
- A.R.C. = +ve implies
1) secant is rising right
2) generally an interval of increase (increasing y-values)
- A.R.C. = -ve implies
1) secant is falling right
2) generally an interval of decrease (decreasing y-values)

5. Average Rates of Change
For Linear Functions:
- R.o.C. is constant
- equals the slope of the linear function

6. Modeling Example #4 on p. 74
h(t) = -5t2 + 10t + 120, t ”belongs to the real interval of” (4, 5)
A.R.C. = =
“Therefore” between 4s & 5s, the height of the rock is decreasing at an average rate of 35m/s

7. Now try the following!
Read: p.68-74
Do: p.76 #24,9,10,13,15