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

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

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

Consider: max decreasing increasing increasing min

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

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

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

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

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

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

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

Homework Page 187 # 10-12, 14, 18-42 even And Worksheet 3-B