Only #6 a&b Use the given graph of f to find the following. The open intervals o
ID: 2882748 • Letter: O
Question
Only #6 a&bUse the given graph of f to find the following. The open intervals on which f is increasing. The open intervals on which f is decreasing. The open intervals on which f is concave upward. The open intervals on which f is concave downward. The coordinates of the points of inflection. Suppose you are given a formula for a function f- (a) How do you determine where f is increasing or decreasing? (b) How do you determine where the graph of f is concave upward or concave downward? (c) How do you locate inflection points? (a) State the First Derivative Test. (b) State the Second Derivative Test. Under what circumstances is it inconclusive? What do you do if it fails? The graph of the derivative f' of a function f is shown. (a) On what intervals is f increasing decreasing? (b) At what values of x does f have a local maximum or minimum? In each part state the x-coordinates of the inflection point of f. Give reasons for your answers. (a) The curve is the graph of f. (b)
Explanation / Answer
(a)
f is increasing for values of x for which f ' is positive. The set of these x values is given by the intervals
(0,1) U (5, 7)
f is decreasing for values of x for which f ' is negative. The set of these x values is given by the intervals
(1,5) U (7,8)
b)
f has a local maximum at values of x for which f '(x) = 0 and f ' changes from positive to negative. Hence f has a maximum at
x= 1 and x=7
f has a local minimum at values of x for which f '(x) = 0 and f ' changes from negative to positive. Hence f has a maximum at
x=5
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