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 function  y = f(x)  given in the figure. The x y-coordinate 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 point A on the positive y-axis, goes down and right, passes through the point B, changes direction at point C, goes up and right, passes through point D, changes direction at point E, goes down and right and exits the window in the first quadrant. Interval a begins at the first unlabeled point and ends at the second unlabeled point. Interval b begins at the first unlabeled point and ends at point A. Interval c begins at point A and ends at point C. Interval d begins at point C and ends at point E. (a) Over what interval(s) (a) through (d) is the rate of change of f(x) positive? (Select all that apply.) abcd (b) Over what interval(s) (a) through (d) is the rate of change of f(x) negative? (Select all that apply.) abcd (c) At what point(s) A through E is the rate of change of f(x) equal to zero? (Select all that apply.) ABCDE

y = f(x)

The x y-coordinate 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 point A on the positive y-axis, goes down and right, passes through the point B, changes direction at point C, goes up and right, passes through point D, changes direction at point E, goes down and right and exits the window in the first quadrant.
• Interval a begins at the first unlabeled point and ends at the second unlabeled point.
• Interval b begins at the first unlabeled point and ends at point A.
• Interval c begins at point A and ends at point C.
• Interval d begins at point C and ends at point E.

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

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

(c) At what point(s) A through E is the rate of change of f(x) equal to zero? (Select all that apply.)