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 & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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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