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Consider the three points (2, 4), (4, 6), and (-2,7). (a) Supposed that at (2,4), we know that f₂z = fy = 0 and fzz > 0, fyy < 0, and fzy = 0. What can we conclude about the behavior of this function near the point (2,4)? ? (b) Supposed that at (4,6), we know that ƒ₂ = fy = 0 and ƒzz > 0, fyy > 0, and fzy = 0. What can we conclude about the behavior of this function near the point (4, 6)?? (c) Supposed that at (-2,7), we know that fz = fy = 0 and fzz < 0, fyy > 0, and fzy = 0. What can we conclude about the behavior of this function near the point (-2,7)?? Using this information, on a separate sheet of paper sketch a possible contour diagram for f.

Consider the three points (2, 4), (4, 6), and (-2,7). (a) Supposed that at (2,4), we know that f₂z = fy = 0 and fzz > 0, fyy < 0, and fzy = 0. What can we conclude about the behavior of this function near the point (2,4)? ? (b) Supposed that at (4,6), we know that ƒ₂ = fy = 0 and ƒzz > 0, fyy > 0, and fzy = 0. What can we conclude about the behavior of this function near the point (4, 6)?? (c) Supposed that at (-2,7), we know that fz = fy = 0 and fzz < 0, fyy > 0, and fzy = 0. What can we conclude about the behavior of this function near the point (-2,7)?? Using this information, on a separate sheet of paper sketch a possible contour diagram for f.

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 three points (2, 4), (4, 6), and (−2, 7). (a) Supposed that at (2,4), we know that ƒz = fy = 0 and ƒzz > 0, fyy < 0, and fzy = 0. What can we conclude about the behavior of this function near the point (2,4)? ? (b) Supposed that at (4,6), we know that få = fy = 0 and fzz > 0, fyy > 0, and ƒzy = 0. What can we conclude about the behavior of this function near the point (4, 6)?? (c) Supposed that at (–2,7), we know that ƒz = fy = 0 and ƒzz < 0, fyy > 0, and ƒzy = 0. What can we conclude about the behavior of this function near the point (-2, 7)?? Using this information, on a separate sheet of paper sketch a possible contour diagram for f.
Transcribed Image Text:Consider the three points (2, 4), (4, 6), and (−2, 7). (a) Supposed that at (2,4), we know that ƒz = fy = 0 and ƒzz > 0, fyy < 0, and fzy = 0. What can we conclude about the behavior of this function near the point (2,4)? ? (b) Supposed that at (4,6), we know that få = fy = 0 and fzz > 0, fyy > 0, and ƒzy = 0. What can we conclude about the behavior of this function near the point (4, 6)?? (c) Supposed that at (–2,7), we know that ƒz = fy = 0 and ƒzz < 0, fyy > 0, and ƒzy = 0. What can we conclude about the behavior of this function near the point (-2, 7)?? Using this information, on a separate sheet of paper sketch a possible contour diagram for f.
Consider the three points (2, 4), (4, 6), and (−2, 7). (a) Supposed that at (2, 4), we know that ƒz = fy = 0 and ƒzz > 0, fyy < 0, and ƒzy = 0. What can we conclude about the behavior of this function near the point (2,4)?? (b) Supposed point (4,6)? (2,4) is a local maximum (2,4) is a local minimum (c) Supposed (2,4) is a saddle point point (-2, 7) (2,4) is a none of these Using this information, on a separate sheet of paper sketch a possible contour diagram for f. ; fz = fy = 0 and ƒzz > 0, fyy > 0, and fry = 0. What can we conclude about the behavior of this function near the at ƒz = fy = 0 and fzx < 0, fyy > 0, and fry = 0. What can we conclude about the behavior of this function near the
Transcribed Image Text:Consider the three points (2, 4), (4, 6), and (−2, 7). (a) Supposed that at (2, 4), we know that ƒz = fy = 0 and ƒzz > 0, fyy < 0, and ƒzy = 0. What can we conclude about the behavior of this function near the point (2,4)?? (b) Supposed point (4,6)? (2,4) is a local maximum (2,4) is a local minimum (c) Supposed (2,4) is a saddle point point (-2, 7) (2,4) is a none of these Using this information, on a separate sheet of paper sketch a possible contour diagram for f. ; fz = fy = 0 and ƒzz > 0, fyy > 0, and fry = 0. What can we conclude about the behavior of this function near the at ƒz = fy = 0 and fzx < 0, fyy > 0, and fry = 0. What can we conclude about the behavior of this function near the
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