The function f(x,y,z)=2x−9y+6z has an absolute maximum value and absolute minimum value subject to the constraint x^2+y^2+z^2=121. Use Lagrange multipliers to find these values. a) Find the maximum b) find the minimum

The function f(x,y,z)=2x−9y+6z has an absolute maximum value and absolute minimum value subject to the constraint x^2+y^2+z^2=121. Use Lagrange multipliers to find these values. a) Find the maximum b) find the minimum

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter11: Introduction To Trigonometry

Section11.4: Applications With Acute Triangles

Problem 45E

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Question

The function

f(x,y,z)=2x−9y+6z

has an absolute maximum value and absolute minimum value subject to the constraint

x^2+y^2+z^2=121.

Use Lagrange multipliers to find these values.

a) Find the maximum

b) find the minimum

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