Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.1 Exercises: 30

Answer

$\\y=\frac{1}{4}x+\frac{3}{4}$

Work Step by Step

$\\f(x)=\sqrt {x-1}$ $\\f(x)={(x-1)}^{1/2}$ $\\f’(x)=\frac{1}{2}(x-1)^{\frac{-1}{2}}$ $\\f’(x)=\frac{1}{2\sqrt {x-1}}$ $\\f’(5)=\frac{1}{2\sqrt {5-1}}$ $\\f’(5)=\frac{1}{4}$ Apply to straight line equation (y-y1)=m(x-x1) $\\y-2=\frac{1}{4}(x-5)$ $\\y-2=\frac{1}{4}x-\frac{5}{4}$ $\\y=\frac{1}{4}x+\frac{3}{4}$
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