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Consider the function f(x, y) = 24.x² – 13y? + 12.ry over the unit square 0

Consider the function f(x, y) = 24.x² – 13y? + 12.ry over the unit square 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the function f(x, y) = 24.x² – 13y? + 12.ry over the unit square 0 <x < 1, 0 < y < 1. NOTE: Enter the exact answer. (a) Find the maximum and minimum values of f on each edge of the square. Maximum Minimum Edge x = 0: f(x, y) f (x, y) Edge x = 1: f(x, y) = f (x, y) = Edge y = 0: f(x, y) : f(x, y) Edge y = 1: f (x,y) f (x, y) = %3D (b) Find the maximum and minimum values of f on each diagonal of the square. Maximum Minimum y = x: f(x, y) = f (x, y) y = 1 – x : f(x, y) = f (x, y) = (c) Find the maximum and minimum values of f on the entire square. Maximum Minimum Entire square f(x,y) : f(x, y) =
Transcribed Image Text:Consider the function f(x, y) = 24.x² – 13y? + 12.ry over the unit square 0 <x < 1, 0 < y < 1. NOTE: Enter the exact answer. (a) Find the maximum and minimum values of f on each edge of the square. Maximum Minimum Edge x = 0: f(x, y) f (x, y) Edge x = 1: f(x, y) = f (x, y) = Edge y = 0: f(x, y) : f(x, y) Edge y = 1: f (x,y) f (x, y) = %3D (b) Find the maximum and minimum values of f on each diagonal of the square. Maximum Minimum y = x: f(x, y) = f (x, y) y = 1 – x : f(x, y) = f (x, y) = (c) Find the maximum and minimum values of f on the entire square. Maximum Minimum Entire square f(x,y) : f(x, y) =
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