(a) Draw contours of f(x, y) = 2x + y for z = −7, −5, −3, −1, 1, 3, 5, 7. (b) On the same axes, graph the constraint x2 +y2 = 5. (c) Use the graph to approximate the points at which f has a maximum or a minimum value subject to the constraint x2 + y2 = 5. (d) Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y subject to x2 + y2 = 5.
(a) Draw contours of f(x, y) = 2x + y for z = −7, −5, −3, −1, 1, 3, 5, 7. (b) On the same axes, graph the constraint x2 +y2 = 5. (c) Use the graph to approximate the points at which f has a maximum or a minimum value subject to the constraint x2 + y2 = 5. (d) Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y subject to x2 + y2 = 5.
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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(a) Draw contours of f(x, y) = 2x + y for z = −7, −5, −3, −1, 1, 3, 5, 7.
(b) On the same axes, graph the constraint x2 +y2 = 5.
(c) Use the graph to approximate the points at which f has a maximum or a minimum value subject to the constraint x2 + y2 = 5.
(d) Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y subject to x2 + y2 = 5.
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