Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.9 Linear Approximations and Differentials - 2.9 Exercises - Page 192: 4


$y-1 = -1/8*(x-3)$

Work Step by Step

The derivative of the function should give us the slope. $$f'(x) = -(x^2-5)^{-3/2}, f'(3) = -4^{-1.5} = -1/8$$ We also find a point it goes through by plugging in $a=3 $to f(x) instead of f'(x) $$f(3) = 1$$ In point slope form, $y-1 = -1/8*(x-3)$
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