Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint. Also, find the points at which these extreme values occur. f(x, y, z) = xyz; x² + y? + z? = 27 The maximum value of f is i The minimum value of f is i The extreme values occur when x = ± i ,y = ± i and z = ± i

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.8: Systems Of Linear Inequalities
Problem 2E
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Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint. Also, find the points at which
these extreme values occur.
f(x, y, z) = xyz; x² + y? + z? = 27
The maximum value of f is i
The minimum value of f is i
The extreme values occur when x = ±
i
,y = ±
i
and z = ±
i
Transcribed Image Text:Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint. Also, find the points at which these extreme values occur. f(x, y, z) = xyz; x² + y? + z? = 27 The maximum value of f is i The minimum value of f is i The extreme values occur when x = ± i ,y = ± i and z = ± i
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