Return on Software: Maximizing the Return on Your Software Investment

Appendix D. Derivatives

This appendix is a refresher on derivatives. The derivative of a function f(x) is another function f″(x) that describes the slope of the line tangent to f(x) at corresponding values of x. Figure D.1 shows an example function f(x) and its derivative function f″(x). Notice that f(x) has a negative (downward) but decreasingly so slope at smaller values of x and that the derivative function f″(x) has correspondingly negative but closer-to-0 values over that same range. For larger values of x, f(x) has a positive (upward) and increasingly so slope and that the derivative function f″(x) has increasingly positive values.

Figure D.1. An example function, f(x), and its derivative, f″(x)

In Figure D.1, there is a value of x where ...