9.3/6

Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other. Consider the graph of the functiony=f(x)

given in the figure.Thexycoordinate plane is given. There is a curve with seven points on the curve (2 unlabeled and 5 labeled) and four labeled intervals on the graph.

• The curve enters the window in the second quadrant, goes up and right, passes through the first unlabeled point, passes through the second unlabeled point, changes direction at pointAon the positivey-axis,goes down and right, passes through the pointB, changes direction at pointC, goes up and right, passes through pointD, changes direction at pointE, goes down and right and exits the window in the first quadrant.
• Intervalabegins at the first unlabeled point and ends at the second unlabeled point.
• Intervalbbegins at the first unlabeled point and ends at pointA.
• Intervalcbegins at pointAand ends at pointC.
• Intervaldbegins at pointCand ends at pointE.

(a) Over what interval(s) (a) through (d) is the rate of change off(x) positive? (Select all that apply.)

a

b

c

d

(b) Over what interval(s) (a) through (d) is the rate of change off(x) negative? (Select all that apply.)

a

b

c

d

(c) At what point(s)AthroughEis the rate of change off(x) equal to zero? (Select all that apply.)

A

B

C

D

E