2nd Derivative of Revenue

Question

What does the second derivative of a revenue function say about the revenue of selling one more?

for example: what does R”(10) say about R(11)?

Answer 1

The first derivative of the revenue function just means how much your revenue will change at each unit. For example, R(10) = 12 just means that your total revenue increases by 12 at the 10th unit. The second derivative of revenue, R''(x), is describing the change in the revenue change. For example, if my revenue goes up by 12 at unit 10 (R'(10) = 12), then I will receive less revenue at the next unit if R''(10) < 0, thus R'(11) < 12.