This file is part of a distribution of the Calculus Applets website (http://www.calculusapplets.com) (v1.1) which has been reformatted for the needs of this OpenCourseware course.
We can generalize the concept of average velocity to any function, not just to a position versus time function. We can define the average rate of change of a function, f, on an interval from a to a + h as . This ration is called the difference quotient and is the change in the output of the function divided by the change in the input. We can similarly extend the concept of instantaneous velocity to the instantaneous rate of change of a function by taking the limit of the difference qoutient as h approaches 0. Specifically, we define the rate of change of function f at a, called the derivative of f at a and written f ' (a), as:
The function f is said to be differentiable at a if this limit exists.
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© Copyright 2001 David J. Eck
© Copyright 2007 Thomas S. Downey
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