Calculus: Early Transcendentals 8th Edition

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

Chapter 14 - Section 14.7 - Maximum and Minimum Values - 14.7 Exercise - Page 969: 46


$(4,4,4)$ and Minimum value is $48$

Work Step by Step

Lagrange Multipliers Method: $F(x,y,z)=x^2+y^2+z^2, G(x,y,z)=x+y+z=12$ This gives $\lambda =2x$ $\lambda =2y$ $\lambda =2z$ Thus, $x=y=z=\dfrac{\lambda}{2}$ After solving for $x$, we get $x=4$ Now, Hence, $x=4,y=4,z=4$ and Minimum value: $x^2+y^2+z^2=48$
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