Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 14 - Partial Derivatives - 14.7 Exercises - Page 979: 42

Answer

$(0,3,0), (0,-3,0)$

Work Step by Step

Formula to calculate the distance is: $D^2=x^2+y^2+z^2$ Also, $F=D^2=x^2+y^2+z^2$ This implies, $F_x=2x+z, F_z=x+2z$ After solving for $x$ and $z$, we get $x=0$ and $z=0$ Thus, $y^2=9+xz=9$ $\implies y=\pm 3$ The required points are: $(0,3,0), (0,-3,0)$
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