The graph of the derivative f ' of a continuous function f is shown below.
http://i36.tinypic.com/2d7btaf.gif <--the graph
1)On what interval(s) is f increasing? (Select all that apply.)
(0,1)
(0,2)
(1,6)
(5,7)
(6,8)
(7,9)
(8,9)
2) On what interval(s) is f decreasing? (Select all that apply.)
(0,1)
(0,2)
(1,6)
(5,7)
(6,8)
(7,9)
(8,9)
3) At what value(s) of x does f have a local maximum? (Select all that apply.)
0
1
2
3
5
6
7
8
4) At what value(s) of x does f have a local minimum? (Select all that apply.)
1
2
3
5
6
7
8
http://i36.tinypic.com/2d7btaf.gif <--the graph
1)On what interval(s) is f increasing? (Select all that apply.)
(0,1)
(0,2)
(1,6)
(5,7)
(6,8)
(7,9)
(8,9)
2) On what interval(s) is f decreasing? (Select all that apply.)
(0,1)
(0,2)
(1,6)
(5,7)
(6,8)
(7,9)
(8,9)
3) At what value(s) of x does f have a local maximum? (Select all that apply.)
0
1
2
3
5
6
7
8
4) At what value(s) of x does f have a local minimum? (Select all that apply.)
1
2
3
5
6
7
8
-
Had to stop and think about this for a bit.
Increasing: the function is increasing where the derivative is positive: (1,6),(8,9)
Decreasing: the function is decreasing where the derivative is negative: (0,1),(6,8)
Local Max: Derivative=0, change from positive to negative (6)
Local Min: Derivative=0, change from negative to positive (1),(8)
Points 2,3,5 and 7 are inflection points (not included in this question)
Increasing: the function is increasing where the derivative is positive: (1,6),(8,9)
Decreasing: the function is decreasing where the derivative is negative: (0,1),(6,8)
Local Max: Derivative=0, change from positive to negative (6)
Local Min: Derivative=0, change from negative to positive (1),(8)
Points 2,3,5 and 7 are inflection points (not included in this question)