concavity and rates of change lesson 2.5. changing rate of change note that the rate of change of...
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Concavity and Rates of Change
Lesson 2.5
Changing Rate of Change
Note that the rate of change of the curve of the top of the gate is changing
Consider how it is changing …
Increasing?
Decreasing?
What effect does that have on the curve?
Consider how it is changing …
Increasing?
Decreasing?
What effect does that have on the curve?
Concavity and Rates of Change
What do the graphs below have in common?
How are they different? Specifically, look at the changing rate of change
Both are increasing functions
The slope (rate of change) is increasing
The slope (rate of change) is decreasing
Concavity and Rates of Change
An increasing positiverate of change is concave UP
A decreasing positiverate of change isconcave DOWN
Slope is becoming less positive
Slope is becoming more positive
Concavity and Rates of Change
Increasing negativerate of change is concave DOWN
Decreasing negativerate of change isconcave UP
Slope is becoming less negative
Slope is becoming more negative
Try It Out
Given the following table Calculate the rates of change for successive pairs of
points – are the slopes increasing or decreasing? Predict concave up or down
Now Plot the points Concave up or concave down?
x 12 15 18 21
H(x) 21.40 21.53 21.75 22.02
Assignment
Lesson 2.5 Page 86 Exercises 1 – 19 odd
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