Recognizing degrees of flexibility with inelastic or elastic

42 Part I: The Nature of Managerial Economics

Consider the following quadratic relationship,

I graph this specific function in Figure 3-1. The derivative of this function is

The symbol dy/dx represents the derivative of variable y taken with respect to variable x. In other words, this is the change in y that occurs given a change in x. In Figure 3-1, the derivative is the slope of the function or line. The change in y is often referred to as the rise, and the change in x is the run. Thus, the derivative is the rise over the run — the function’s slope.

Figure 3-1: Derivative and slope for y=x2 .

For any given value of x, the slope of the original function at that point can be determined by substituting x’s value into the derivative. For example, at x equals 4, the original function’s slope is 8. The tangent illustrating the slope at x equals 4 is illustrated in the figure.

Rules, rules everywhere

Okay, enough general comments on derivatives. This section reviews basic differentiation rules that you use in managerial economics. Again, I assume you already know calculus — this is just a brief refresher for some of the