Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.5 - Implicit Differentiation - 3.5 Exercises - Page 216: 43

Answer

$(-2.29129,1.24514);\hspace{1cm}(-2.29129,-1.24514)$ $(2.29129,-1.24514);\hspace{1cm}(2.29129,1.24514)$

Work Step by Step

The lemniscate equation is: $2(x^2+y^2)^2=25(x^2-y^2)$ $2x^4+4x^2y^2+2y^4=25x^2-25y^2$ Take the derivative $8x^3+8xy^2+8x^2y\frac{dy}{dx}+8y^3\frac{dy}{dx}=50x-50y\frac{dy}{dx}$ $\frac{dy}{dx}=\frac{50x-8xy^2-8x^3}{8y^3+8xy^2+50y}$ $50x-8xy^2-8x^3=0$ $x=-2.29129;\hspace{5mm}x=2.29129$ $(-2.29129,1.24514);\hspace{1cm}(-2.29129,-1.24514)$ $(2.29129,-1.24514);\hspace{1cm}(2.29129,1.24514)$
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