Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. We recommend using aĪuthors: Gilbert Strang, Edwin “Jed” Herman Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses theĬreative Commons Attribution-NonCommercial-ShareAlike License If f ( x ) f ( x ) is a function defined on an interval, , then the amount of change of f ( x ) f ( x ) over the interval is the change in the y y values of the function over that interval and is given by One application for derivatives is to estimate an unknown value of a function at a point by using a known value of a function at some given point together with its rate of change at the given point. We can apply this general principle to any function given by an equation y f(x). These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics. average velocity for a position function s(t), which describes the. In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function.
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