Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 103: 26


$$ f(5+h)=\sqrt{5+h}$$ $$\frac{f(a+h)-f(a)}{h} =\sqrt{6}-\sqrt{5}$$

Work Step by Step

Since $ f(x)=\sqrt{x}$, then $ f(5+h)=\sqrt{5+h}$. The quotient difference is given by $$\frac{f(a+h)-f(a)}{h}=\frac{f(6)-f(5)}{1}=\sqrt{6}-\sqrt{5}=\sqrt{6}-\sqrt{5}$$
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