Answered: Consider a function f(x,y)=4x^2+y^2 .…

Consider a function f(x,y)=4x^2+y^2 . Find the minimum value of this function subject to the constraint g(x,y)=x+2y−3=0.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 1YT

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Question

Consider a function f(x,y)=4x^2+y^2 .

Find the minimum value of this function subject to the constraint g(x,y)=x+2y−3=0.

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Step 1: Conceptual Introduction

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Step 2: Construct the Lagrangian

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Step 3: Setting Partial Derivatives to Zero

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Step 4: Solve the System of Equations:

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Step 5: Minimum Value of the Function

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Solution

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