Second Derivative

Question

In March of 2009, when the U.S. was in a major recession, an Economist columnist wrote, "but is it possible to take comfort from the fact that conditions are deteriorating less alarmingly? Economists call this the second derivative." Explain how this relates to what you've learned about the second derivative. Draw a graph to aid in your explanation

Answer 1

The second derivative is the rate of change of the derivative. For a position function the first derivative is velocity (how fast your position is changing) and the second derivative is acceleration (are you speeding up or slowing down).

In the example above the derivative is whether the economy is increasing or decreasing but the second derivative is whether that rate is speeding up or slowing down. In a graph the second derivative is the concavity so the graph of the economy would be decreasing but concave up, it is still going down, but less steeply with time.