1. Key Concept 1

2. Analyze Increasing and Decreasing Behavior
A. Use the graph of the function f (x) = x 2 – 4 to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically.
Example 1

3. Answer: f (x) is decreasing on and increasing on .
Analyze Increasing and Decreasing Behavior
Answer: f (x) is decreasing on and increasing on
Example 1

4. Analyze Increasing and Decreasing Behavior
B. Use the graph of the function f (x) = –x 3 + x to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically.
Example 1

5. Answer: f (x) is decreasing on and and increasing on
Analyze Increasing and Decreasing Behavior
The table shows that as x increases to , f (x) decreases; as x increases from , f (x) increases; as x increases from , f (x) decreases. This supports the conjecture.
Answer: f (x) is decreasing on and
and increasing on
Example 1

6. A. f (x) is increasing on (–∞, –1) and (–1, ∞).
Use the graph of the function f (x) = 2x 2 + 3x – 1 to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically.
A. f (x) is increasing on (–∞, –1) and (–1, ∞).
B. f (x) is increasing on (–∞, –1) and decreasing on (–1, ∞).
C. f (x) is decreasing on (–∞, –1) and increasing on (–1, ∞).
D. f (x) is decreasing on (–∞, –1) and decreasing on (–1, ∞).
Example 1

7. Key Concept3

8. Substitute –3 for x1 and –1 for x2.
Find Average Rates of Change
A. Find the average rate of change of f (x) = –2x 2 + 4x + 6 on the interval [–3, –1].
Use the Slope Formula to find the average rate of change of f on the interval [–3, –1].
Substitute –3 for x1 and –1 for x2.
Evaluate f(–1) and f(–3).
Example 5

9. Find Average Rates of Change
Simplify.
The average rate of change on the interval [–3, –1] is 12. The graph of the secant line supports this conclusion.
Answer: 12
Example 5

10. Substitute 2 for x1 and 5 for x2.
Find Average Rates of Change
B. Find the average rate of change of f (x) = –2x 2 + 4x + 6 on the interval [2, 5].
Use the Slope Formula to find the average rate of change of f on the interval [2, 5].
Substitute 2 for x1 and 5 for x2.
Evaluate f(5) and f(2).
Example 5

11. Find Average Rates of Change
Simplify.
The average rate of change on the interval [2, 5] is –10. The graph of the secant line supports this conclusion.
Answer: –10
Example 5

12. Find the average rate of change of f (x) = –3x 3+ 2x + 3 on the interval [–2, –1].
B. 11 C.
D. –19
Example 5