Calculus - Standalone book
3rd Edition
ISBN: 9781464125263
Author: Jon Rogawski, Colin Adams
Publisher: W.H. Freeman & Co
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Question
Chapter 15.8, Problem 1E
To determine
We need to find the extreme values of the function subject to the constraint .
a. Show that the Lagrange equation gives and
b. Show that these equations imply and .
c. Use the constraint equation to determine the possible critical points .
d. Evaluate at the critical points and determine the minimum and maximum values.
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Consider the function f(x,y) = x^2 + y^2 subject to the constraint g(x, y) = x + y - 3 = 0. Use the Lagrange Multiplier method to find the minimum value of f(x, y) subject to the constraint g(x, y) = 0.
find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the planes 2x-y = 0 and y + z = 0
Can this problem be solved using lagrange multipliers?
Consider the function f(x, y) = x2 + 3y2 + 2y
on the closed disk S: x2 + y2 < 1.
a) Find the critical points in the interior of S using the first and second derivative tests, and decide if they are local maxima, minima, or neither.
b) Find the maximum and minimum of f(x, y) on the boundary of S by using Lagrange multipliers on the boundary of S. (i.e. optimize f(x, y) subject tothe constraint x2 + y2 = 1).(c) Using the results of (a) and (b), conclude what the global maximum and minimum values of f(x, y) are, and where they are attained.
Chapter 15 Solutions
Calculus - Standalone book
Ch. 15.1 - Prob. 1PQCh. 15.1 - Prob. 2PQCh. 15.1 - Prob. 3PQCh. 15.1 - Prob. 4PQCh. 15.1 - Prob. 5PQCh. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5E
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