1. Honors Precalculus October 17-18, 2016 Mrs. Agnew
Rates of Change
Honors Precalculus
October 17-18, 2016
Mrs. Agnew

2. Essential Question Essential Vocabulary
How do you find the average rate of change of a function?
Essential Vocabulary
Average Rate of Change
Function
Function Notation

3. Average Rate of Change
The rate of change of a given function from a to b is given by:
Average Rate of Change: rate at which the values of a function change as the variable changes.
Example: Average speed

4. Rates of Change
Rates of change for linear functions are constant (rate of change = slope).
Rate of change varies for all other functions.
Let’s find the rates of change for different functions… examples.

5. Average Rate of Change
The average rate of change gives the slope of a SECANT line between x=a and x=b.
Let’s examine the graph of the AROC and a calculus expression known as the DIFFERENCE QUOTIENT.

6. Homework:
page 90 – 92
#61, 65, 68
77(c,d,e,f), 81 – 87 (Odd; only part a: Use Difference Quotient to find the AROC from a to a+h)

7. Increasing and Decreasing
A function is said to be increasing when the graph has a positive slope.
In other words, the graph is rising.
A function is said to be decreasing when the graph has a negative slope.
In other words, the graph is falling.

8. Extreme Values
An extreme value is a maximum or minimum value of a function
Local extrema vs. absolute extrema
Maximum values occur when the function changes from increasing to decreasing
Minimum values occur when the function changes from decreasing to increasing.

9. Homework:
Worksheet Provided