1. Rates of Change Lesson 1.2

2. 2 Which Is Best?  Which roller coaster would you rather ride?  Why? Today we will look at a mathematical explanation for why one is preferable to another.

3. 3 Rate of Change  Given function y = 3x + 5 xy 05 18 211 314 417 6 2

4. 4 Rate of Change  Try calculating for different pairs of (x, y) points  You should discover that the rate of change is constant xy 05 18 211 314 417

5. 5 Rate of Change  Consider the function  Enter into Y= screen of calculator  View tables on calculator (  Y) You may need to specify the beginning x value and the increment

6. 6 Rate of Change  As before, determine the rate of change for different sets of ordered pairs xsqrt(x) 00.00 11.00 21.41 31.73 42.00 52.24 62.45 72.65

7. 7 Rate of Change  View spreadsheet which demonstrates results of the formula below.spreadsheet

8. 8 Rate of Change (NOT a constant)  You should find that the rate of change is changing – NOT a constant.  Contrast to the first function y = 3x + 5

9. 9 Function Defined by a Table  Consider the two functions defined by the table The independent variable is the year.  Predict whether or not the rate of change is constant  Determine the average rate of change for various pairs of (year, sales) values Year1982198419861988199019921994 CD sales05.853150287408662 LP sales24420512572122.31.9

10. 10 Increasing, Decreasing Functions  Note that for the CD sales, the rates of change were always positive  For the LP sales, the rates of change were always negative An increasing function A decreasing function

11. 11 Increasing, Decreasing Functions An increasing functionA decreasing function

12. 12 Increasing, Decreasing Functions Given Q = f ( t )  A function, f is an increasing function if the values of f increase as t increases The average rate of change > 0  A function, f is an decreasing function if the values of f decrease as t increases The average rate of change < 0

13. 13 Using TI to Find Rate Of Change  Define a function f(x) 3*x + 5 -> f(x)  We want to define the function and assign it to a function Use the STO> key

14. 14 Using TI to Find Rate Of Change  Now call the function difquo( a, b ) using two different x values for a and b  For rate of change of a different function, redefine f(x)

15. 15 Assignment  Lesson 1.2  Page 15  Exercises 3, 5, 7, 9, 11, 12, 13, 15, 21