Section 3.1

Increasing and Decreasing Functions

Examples

1) Give the intervals where the function is increasing and decreasing.

Decreasing:

Increasing:

2) Give the intervals where the function increasing and decreasing

Increasing: Decreasing:

Test for increasing and decreasing functions

Let f be a differentiable function on the interval

1) If for all x in (a,b), then f is increasing on (a,b)

2) If for all x in (a,b), then f is decreasing on (a,b)

3) If for all x in (a,b), then f is constant on (a,b)

1) Give the intervals where the function is increasing and decreasing

Interval
Test Value	x = -1	x = 3
Sign of	Negative	Positive
Conclusion	Decreasing	Increasing

2) Find the intervals where the function is decreasing and increasing

Interval
Test Value	x = -1	x = 1
Sign of	Positive	Positive
Conclusion	Increasing	Increasing

3) Find the intervals where the function is increasing or decreasing.

Interval
Test Value	x = -1	x = 1	x = 3
Sign of	Positive	Negative	Positive
Conclusion	Increasing	Decreasing	Increasing

4) Find the intervals where the functions is increasing and decreasing

Interval
Test Value	x = -1	x = 1
Sign of	Negative	Positive
Conclusion	Decreasing	Increasing