12. The function f(x,y,z) = (xyz)1/2 x+y+z=9 with x20, y 20, and z20. Use Lagrange multipliers to find these values. has an absolute maximum value and absolute minimum value subject to the constraint The absolute maximum value is The absolute minimum value is

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter9: Quadratic Functions And Equations
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to0eobul afan-tea T
12. The function f(x,y,z) = (xyz)'² has an absolute maximum value and absolute minimum value subject to the constraint
x+y+z=9with x20, y20, and z20. Use Lagrange multipliers to find these values.
The absolute maximum value is
The absolute minimum value is
13. Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in
the ellipse 32x2 + 2y2 = 32.
%3D
Let length be the dimension parallel to the x-axis and let width be the dimension parallel to the y-axis.
Length
%3D
Width =
(Type exact answers, using radicals as needed.)
14. Find the point on the plane 4x +7y +8z- 16=0 closest to the point
Transcribed Image Text:to0eobul afan-tea T 12. The function f(x,y,z) = (xyz)'² has an absolute maximum value and absolute minimum value subject to the constraint x+y+z=9with x20, y20, and z20. Use Lagrange multipliers to find these values. The absolute maximum value is The absolute minimum value is 13. Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 32x2 + 2y2 = 32. %3D Let length be the dimension parallel to the x-axis and let width be the dimension parallel to the y-axis. Length %3D Width = (Type exact answers, using radicals as needed.) 14. Find the point on the plane 4x +7y +8z- 16=0 closest to the point
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