Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint. Also, find the points at which chese extreme values occur. f(x, y, z) = 7x + y – 69z; x² + y² + z² = 307904 NOTE: Enter the exact answer. Лахimum : at (?, ?,?) Minimum : at |(?,?,?)

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 36E
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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) = 7x + y – 69z;
x2 + y? + z? = 307904
%3D
NOTE: Enter the exact answer.
Maximum :
at (?, ?, ?)
Minimum :
at (?, ?, ?)
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) = 7x + y – 69z; x2 + y? + z? = 307904 %3D NOTE: Enter the exact answer. Maximum : at (?, ?, ?) Minimum : at (?, ?, ?)
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