Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Section 11.4 - Introduction to Derrivatives - Concept and Vocabulary Check - Page 1174: 4



Work Step by Step

The slope of the tangent line to the graph of a function $y=f\left( x \right)$ at $\left( a,f\left( a \right) \right)$ is given by $\underset{h\to 0}{\mathop{\lim }}\,$ $\frac{f\left( a+h \right)-f\left( a \right)}{h}$ provided that this limit exists. Also, the derivative of the function is given by ${f}'\left( x \right)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f\left( a+h \right)-f\left( a \right)}{h}$. Thus, the derivative of a function $f$ gives the slope of $f$ for any value of x in the domain of $f'$.
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