Use Lagrange multipliers to find the given extremum. Assume that x and y are positive. Minimize f(x, y) = x2 − 4x + y2 − 16y + 42 Constraint: x + y = 24   Minimum of f(x, y) =   at (x, y) =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Use Lagrange multipliers to find the given extremum. Assume that x and y are positive.

Minimize f(x, y) = x2 − 4x + y2 − 16y + 42

Constraint: x + y = 24
 
Minimum of f(x, y) =
 
at (x, y) = 
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