1. Increasing/decreasing and the First Derivative test
Section 3-3
Increasing/decreasing
and the First Derivative test

2. Graphs that are going up or increasing have slopes that are?
POSITIVE
Graphs that are going down or decreasing have slopes that are?
NEGATIVE

3. Increasing and Decreasing
Let f be a differentiable function in the interval (a,b) then
If for x in (a,b), then f is decreasing
If for x in (a,b), then f is increasing
If for x in (a,b), then f is constant and has a horizontal tangent

4. Consider:
max
decreasing
increasing
increasing
min

5. The First Derivative Test
Let f be a differentiable function with
If changes from positive to negative, then f has a relative maximum at c
If changes from negative to positive, then f has a relative minimum at c

6. 1.) Determine the intervals where the function
is increasing and decreasing
 Interval  x
Result

7. 2.) Determine the intervals where the function
is increasing and decreasing
 Interval  x
Result
Def: Strictly Monotonic: A function that is either increasing or decreasing on the entire interval is said to be strictly monotonic

8. 3.) Determine where the function is increasing and decreasing and find
All extrema
 Interval  x
Result

9. 4.) Graph,
then determine where the function
is increasing and decreasing

10. 5.) Classify the relative extrema of
and find the intervals where increasing and decreasing
 Interval  x
Result

11. 6.) Classify the relative extrema of
and find the intervals where increasing and decreasing
 Interval  x
Result

12. Homework
Page 187 # 10-12, 14, even And Worksheet 3-B