1. Use the method of Lagrange multipliers to find the minimum value of the function f(x, y) = x + y² subject to the constraint xy= 54.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 35CR: Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.
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Please slove question 1 and 2. Please solve both.

1. Use the method of Lagrange multipliers to find the minimum value of the function
f (x, y) = x² + y² subject to the constraint
xy = 54.
2. Find and list all critical values and identify the absolute maximum and minimum values
of the function f(x,y)= xy² over the region in the xy-plane bounded by the graphs of
y = 4 – x and y=3x for y> 0.
Transcribed Image Text:1. Use the method of Lagrange multipliers to find the minimum value of the function f (x, y) = x² + y² subject to the constraint xy = 54. 2. Find and list all critical values and identify the absolute maximum and minimum values of the function f(x,y)= xy² over the region in the xy-plane bounded by the graphs of y = 4 – x and y=3x for y> 0.
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