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Tutorial Exercise Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = V 48 – x2 – y2 - Constraint: x + y – 8 = 0 Step 1 Note that f(x, y) = 48 – x2 – y2 has a maximum when g(x, y) = (48 – x² – y²) has a maximum. For - simplicity of the calculations, find the maximum of g. Let the equation of constraint be h(x, y) = x + y – 8 = 0. Find Vg(x, y) and 1Vh(x, y), where 1 is the Lagrange multiplier (a real number). Vg(x, y) = i - 2 j 1Vh(x, y) (i + j)

Tutorial Exercise Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = V 48 – x2 – y2 - Constraint: x + y – 8 = 0 Step 1 Note that f(x, y) = 48 – x2 – y2 has a maximum when g(x, y) = (48 – x² – y²) has a maximum. For - simplicity of the calculations, find the maximum of g. Let the equation of constraint be h(x, y) = x + y – 8 = 0. Find Vg(x, y) and 1Vh(x, y), where 1 is the Lagrange multiplier (a real number). Vg(x, y) = i - 2 j 1Vh(x, y) (i + j)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Tutorial Exercise Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = V 48 – x2 – y2 Constraint: x + y – 8 = 0 Step 1 Note that f(x, y) = V 48 – x2 – y2 has a maximum when g(x, y) = (48 – x² – y2) has a maximum. For %D simplicity of the calculations, find the maximum of g. Let the equation of constraint be h(x, y) = x + y – 8 = 0. Find Vg(x, y) and AVh(x, y), where å is the Lagrange multiplier (a real number). Vg(x, y) i - 2 j AVh(x, y) (i + j)
Transcribed Image Text:Tutorial Exercise Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = V 48 – x2 – y2 Constraint: x + y – 8 = 0 Step 1 Note that f(x, y) = V 48 – x2 – y2 has a maximum when g(x, y) = (48 – x² – y2) has a maximum. For %D simplicity of the calculations, find the maximum of g. Let the equation of constraint be h(x, y) = x + y – 8 = 0. Find Vg(x, y) and AVh(x, y), where å is the Lagrange multiplier (a real number). Vg(x, y) i - 2 j AVh(x, y) (i + j)
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