Find all constrained relative extrema of f(x, y, z) = (x − 1)^2 + (y − 1)^2 + z^2 subjected the constraint 2x − 3y + z = 19. If you get only one constrained relative extremum, then decide if it is a constrained relative maximum or a constrained relative minimum. Justify your answer.

Find all constrained relative extrema of f(x, y, z) = (x − 1)^2 + (y − 1)^2 + z^2 subjected the constraint 2x − 3y + z = 19. If you get only one constrained relative extremum, then decide if it is a constrained relative maximum or a constrained relative minimum. Justify your answer.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 17EQ

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Question

Find all constrained relative extrema of f(x, y, z) = (x − 1)^2 + (y − 1)^2 + z^2
subjected the constraint 2x − 3y + z = 19. If you get only one constrained relative
extremum, then decide if it is a constrained relative maximum or a constrained
relative minimum. Justify your answer.

Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .

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