October 1718 2016 Mrs Agnew Essential Question How do you find the average rate of change of a function Essential Vocabulary Average Rate of Change Function Function Notation Average Rate of Change ID: 789500
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Slide1
Rates of Change
Honors
Precalculus
October 17-18, 2016
Mrs. Agnew
Slide2Essential Question
How do you find the average rate of change of
a function?
Essential Vocabulary
Average Rate of Change
Function
Function Notation
Slide3Average 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
Slide4Rates 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.
Slide5Average 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.
Slide6Homework:
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)
Slide7Increasing 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.
Slide8Extreme 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.
Slide9Homework:
Worksheet Provided