Differentiable Functions and Their Derivatives

  • G. Baley Price

Abstract

One of the important problems in mathematics and in its applications in science and engineering is the following: if y = f(x), find the rate of increase of y with respect to x. For example, if y = 2x + 5, then y0 = 2x0 + 5, y1 = 2x1 + 5, and y1y0 = 2(x1>x0). Thus
$$\frac{{{y_1} - {y_0}}}{{{x_1} - {x_0}}} = 2,$$
(1)
(1) and the rate of increase of y with respect to x is 2. This example shows that the problem has a simple solution in all cases in which f is a linear function. Thus, if y = ax + b, then
$$\frac{{{y_1} - {y_0}}}{{{x_1} - {x_0}}} = 2,$$
(2)
Observe that, for this linear function f, the rate of increase of y with respect to x is the same, namelya, for everyx0 and xl.

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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • G. Baley Price
    • 1
  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

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