Calculus (3rd Edition)

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

Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 172: 16



Work Step by Step

Given $$y=\frac{3-\sqrt{x}}{\sqrt{x+3}}, \quad a=1, \quad d x=-0.1$$ Since \begin{align*} f'(x)&= \frac{\frac{d}{dx}\left(3-\sqrt{x}\right)\sqrt{x+3}-\frac{d}{dx}\left(\sqrt{x+3}\right)\left(3-\sqrt{x}\right)}{\left(\sqrt{x+3}\right)^2}\\ &= \frac{-3\sqrt{x}-3}{2\sqrt{x}\left(x+3\right)\sqrt{x+3}}\\ f'(1)&= - 0.375 \end{align*} Then \begin{align*} \Delta y \approx &= f'(1)dx\\ &= (-0.375)(-0.1)\\ &=0.0375 \end{align*}
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