Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 11: 63

Answer

$f(x)$ is decreasing for all real numbers in the domain of $f(x)$. Also, the domain of $f(x)$ is $R-\{4\}$ (all real numbers except $4$).

Work Step by Step

To find the intervals in which $f(x)$ is increasing, or, decreasing we can use first derivative of $f(x)$. Here, $f(x)=\dfrac{1}{x-4}$, so, $f'(x)=\dfrac{-1}{(x-4)^2}$. Since, $(x-4)^2>0$, thus, $f'(x)<0$ for all $x$ in the domain. Therefore, the function, $f(x)$ is decreasing for all $x$ in the domain by the first derivative test.
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