Let f(r, y) = r² – 2ry+2y² – x + 3. %3D (a) Determine all the critical points of f. (b) Determine the nature of each critical point of f. (c) Determine the maximum and minimum of f on the boundary of the triangle with vertices (0,0), (2,0) and (1, 1). (d) Determine the absolute maximum and minimum of f over the entire triangle with vertices (0,0), (2,0) and (1,1).
Let f(r, y) = r² – 2ry+2y² – x + 3. %3D (a) Determine all the critical points of f. (b) Determine the nature of each critical point of f. (c) Determine the maximum and minimum of f on the boundary of the triangle with vertices (0,0), (2,0) and (1, 1). (d) Determine the absolute maximum and minimum of f over the entire triangle with vertices (0,0), (2,0) and (1,1).
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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Transcribed Image Text:2. Let f(x, y) = x² – 2xy + 2y² – x + 3.
(a) Determine all the critical points of f.
(b) Determine the nature of each critical point of f.
(c) Determine the maximum and minimum of f on the boundary of the triangle with vertices
(0,0), (2,0) and (1, 1).
(d) Determine the absolute maximum and minimum of f over the entire triangle with vertices
(0,0), (2,0) and (1,1).
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