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Rates of Change and Tangent Lines. 2.4. Average Rate of Change. Total Change/Length of the interval Δy / Δ x Like the average velocity this looks like the slope formula Average rate of change is the slope of the secant line. Example.

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Presentation Transcript
average rate of change
Average Rate of Change

Total Change/Length of the interval

Δy/Δx

Like the average velocity this looks like the slope formula

Average rate of change is the slope of the secant line

example
Example

Find the average rate of change of the function f(x) = x3 – x on the interval [1, 3]

example1
Example

Through experiment, biologists have found that the following graph models the population growth of fruit flies over 50 days. Find the average rate of change from day 23 to day 45.

slope of the secant line
Slope of the secant line

The slope of the secant line is the same as the average rate of change. The formula for the slope of the secant line is just the slope formula written in a manor that you should recognize.

C:\Documents and Settings\melli\My Documents\Hon Calc\Chapter 2\secant-tangent.gsp

slope of the secant line1
Slope of the Secant Line

This leads us to be able to find the slope of a tangent line

example2
Example

a) Find the slope of the tangent line at x=2

b) Find the point where the slope is -1/8

homework
Homework

Pg 92 #1-7 odd, #9-12 part a, #19-22

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