Calculus 10th Edition

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

Chapter P - P.2 - Linear Models and Rates of Change - Exercises: 82

Answer

$y=\frac{3x}{4}-6$

Work Step by Step

Original Equation: $(x-1)^{2}+(y-1)^2=25$ Differentiate Implicitly Using Chain Rule: $2(x-1)\frac{dx}{dx}+2(y-1)\frac{dy}{dx}=0$ Simplify: $(2x-2)+(2y-2)\frac{dy}{dx}=0$ $(2y-2)\frac{dy}{dx}=-2x+2$ $\frac{dy}{dx}=\frac{-2x+2}{2y-2}$ $\frac{dy}{dx}=\frac{-x+1}{y-1}$ Plug in $(x,y)$ $\frac{dy}{dx}=\frac{3}{4}$ Point Slope form: $y-y_{1}=\frac{dy}{dx}(x-x_{1})$ Plug in Values: $y+3=\frac{3}{4}(x-4)$ Simplify: $y=\frac{3x}{4}-6$
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