1. Concavity and Rates of Change
Lesson 2.5

2. 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?

3. 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

4. Concavity and Rates of Change
Slope is becoming more positive
An increasing positive rate of change is concave UP
A decreasing positive rate of change is concave DOWN
Slope is becoming less positive

5. Concavity and Rates of Change
Increasing negative rate of change is concave DOWN
Decreasing negative rate of change is concave UP
Slope is becoming more negative
Slope is becoming less negative

6. Try It Out Given the following table Now Plot the points
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

7. Assignment
Lesson 2.5
Page 86
Exercises 1 – 19 odd