Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.1 - Derivatives of Polynomials and Exponential Functions - 3.1 Exercises: 40

Answer

$y=\frac{1}{2}x-\frac{1}{2}$
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Work Step by Step

In order to find the equation of a tangent line, first you need to take the derivative. For this equation, just use the Power Rule. $y=x−\sqrt x$ $y=x−x^{1/2}$ $Power Rule: \frac{dy}{dx}=nx^{n−1}$ $dy/dx=1-\frac{1}{2}x^{-1/2}$ The derivative is your equation of the slope. To find the slope at the point (1,0), plug in x=1 into the derivative equation: $dy/dx \Bigr|_{\substack{x=1}}= 1-\frac{1}{2}(1)^{-1/2} = 1/2.$ Now to get the equation of the tangent line, use point-slope form: $y−y1=m(x−x1)$ $y−(0)=(1/2)(x−(1))$ $y=\frac{1}{2}x-\frac{1}{2}$
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