Sketch a graph that meets the following requirements:

f(x) is decreasing and concave down for x<-2

f(x) is decreasing and concave up for -2<x<0

f(x) is increasing and concave up for 0<x<3

f(x) is increasing and concave down for x>3

At each of the points A, B, and C, determine if GDP is increasing or decreasing.

The maximum and minimum values of a business cycle are called peaks and troughs.

What can you say about the rate of change of GDP at these peaks and troughs?

Is GDP increasing and decreasing at a constant rate? Explain.

At Point D, GDP is increasing. Is the growth in GDP speeding up or slowing down? How do you know?

When is GDP changing the fastest? How can you tell this from the graph?

At Point E, is the slope of the curve negative or positive? What does this mean in the context of this problem?

At Point E, are the slopes increasing or decreasing? What does this tell you about how GDP is changing at this part of the business cycle?

Describe what is happening at Point F with as much detail as possible.

(-∞,-1.5)

x>3.5

(-1.5,1.5)

Is f increasing or decreasing at x = −1? How do you know?

Is the rate of change of f increasing or decreasing at x = −1? How do you know?