circle. -) Use the Lagrange multipliers to find the local extrema of the function f(x, y) = 4x² + y² + z? subject to the constraints 2x – y + z = 4 and a + 2y - z = 1. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please answer 4b only
a)Let T = f(x, y) be the temperature at the point (x, y) on the circle x = cost,
y = sin t, 0<t< 2n; and suppose that
= 8x – 4y and 4 = 8y – .
(i) Find the maximum and minimum temperatures on the circle.
(ii) Suppose T ±4x² – 4xy + 4y², find the maximum and minimum values of T on the
circle.
b) Use the Lagrange multipliers to find the local extrema of the function f(x, y) = 4x² +y² + z²
subject to the constraints 2x – y + z = 4 and x + 2y – z = 1.
%3D
Transcribed Image Text:a)Let T = f(x, y) be the temperature at the point (x, y) on the circle x = cost, y = sin t, 0<t< 2n; and suppose that = 8x – 4y and 4 = 8y – . (i) Find the maximum and minimum temperatures on the circle. (ii) Suppose T ±4x² – 4xy + 4y², find the maximum and minimum values of T on the circle. b) Use the Lagrange multipliers to find the local extrema of the function f(x, y) = 4x² +y² + z² subject to the constraints 2x – y + z = 4 and x + 2y – z = 1. %3D
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