The graph of the derivative f \' of a continuous function f is shown below. http

Question

The graph of the derivative f ' of a continuous function f is shown below.

http://i36.tinypic.com/2d7btaf.gif


(a) 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)
none of these


On what interval(s) is f decreasing? (Select all that apply.)
(0, 1)
(0, 2)
(1, 6)
(2, 3)
(3, 5)
(5, 7)
(6, 8)
(7, 9)
(8, 9)
none of these


(b) At what value(s) of x does f have a local maximum? (Select all that apply.)
0
1
2
3
5
6
7
8
none of these


At what value(s) of x does f have a local minimum? (Select all that apply.)
0
1
2
3
5
6
7
8
none of these

Explanation / Answer

f increases in the region in which it has positive derivative.so it increases in the region (1,6 and (8,9) similarly f decreases when f has negative derivative.so it decreases in the regions (0,1) and (6,8) f has local maximum if derivative of f is 0 and double derivative of is negative ie derivative of f is decreasing.so it has local maximum at 6 f has local minimum if derivative of f is 0 and double derivative of is +ve ie derivative of f is increasing.so it has local minimums at 1&8

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