Question

45 - 46. analyzing slopes use the points a, b, c, d, and e in the following graphs to answer these questions.
a. at which points is the slope of the curve negative?
b. at which points is the slope of the curve positive?
c. using a - e, list the slopes in decreasing order.
45.
46.

Explanation:

Step1: Recall slope - sign rules

The slope of a curve at a point is negative when the curve is decreasing at that point and positive when the curve is increasing.

Step2: Analyze negative - slope points for 45

For the graph in 45, the curve is decreasing at points C and E. So the points with negative slope are C, E.

Step3: Analyze positive - slope points for 45

The curve is increasing at points A and B. So the points with positive slope are A, B.

Step4: Analyze slope at point D for 45

At point D, the tangent to the curve is horizontal, so the slope is 0.

Step5: Order slopes for 45

Since positive slopes are greater than 0 and 0 is greater than negative slopes, and the steeper the positive - sloped part, the larger the positive slope. The slopes in decreasing order are B, A, D, C, E.

Step6: Analyze negative - slope points for 46

For the graph in 46, the curve is decreasing at points D and E. So the points with negative slope are D, E.

Step7: Analyze positive - slope points for 46

The curve is increasing at points A and B. So the points with positive slope are A, B.

Step8: Analyze slope at point C for 46

At point C, the tangent to the curve is horizontal, so the slope is 0.

Step9: Order slopes for 46

The slopes in decreasing order are B, A, C, D, E.

Answer:

45:
a. C, E
b. A, B
c. B, A, D, C, E
46:
a. D, E
b. A, B
c. B, A, C, D, E