egghead's Guide to Calculus by Cara Cantarella

Author:Cara Cantarella
Language: eng
Format: epub
Tags: MATHEMATICS / Calculus
ISBN: 978-0-7689-4061-9
Publisher: Peterson's
Published: 2015-08-12T16:00:00+00:00

We could also rewrite the y-coordinates in function notation. The coordinate y2 would be written as f (x + h). The coordinate y1 would be written as f (x). This would give us the following formula:

As the points y2 and y1 move closer together, the value of h approaches zero. When h equals zero, however, we can no longer use the slope formula, because this would result in division by zero, which is undefined. We get around this problem by using the limit to find the value of the slope:

The limit of the function as h approaches zero is the slope of the tangent line to the curve. We call this slope the derivative.

The derivative is noted using any of the following symbols: . These all mean the same thing: “the derivative of.” The symbol is pronounced “f prime of x.” The symbol is pronounced “y prime.”

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