Calculus 8th Edition

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

Chapter 2 - Derivatives - 2.1 Derivatives and Rates of Change - 2.1 Exercises - Page 113: 7



Work Step by Step

$y=\sqrt x ,(1,1)$ 1. Find the first derivative by using the power rule. Finding the first derivative gives you the slope of the tangent line. $y'=\frac{1}{2\sqrt x}$ 2. Plug in the given x value to find the slope of the tangent line to the curve at the given point. $y'=\frac{1}{2\sqrt 1}$ $y'=\frac{1}{2}$ 3. Now that we have the slope of the tangent line, we can write the equation for that line in point-slope form. $y-y_{1}=m(x-x_{1})$ $y-1=\frac{1}{2}(x-1)$ 4. Rewrite into standard form by distributing the 1/2 and adding one to both sides. $y-1+1=\frac{1}{2}x-\frac{1}{2}+1$ 5. Clean up and simplify. $y=\frac{1}{2}x+\frac{1}{2}$
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