Consider the three points (2, 2), (4,4), and (6, -2). (a) Supposed that at (2, 2), we know that f = fy = 0 and fxx < 0, fyy = 0, and fry < 0. What can we conclude about the behavior of this function near the point (2, 2)? ? + (b) Supposed that at (4,4), we know that fa = fy = 0 and fax < 0, fyy > 0, and fry = 0. What can we conclude about the behavior of this function near the point (4,4)? ? + (c) Supposed that at (6, -2), we know that f = fy = 0 and fxx > 0, fyy < 0, and fry = 0. What can we conclude about the behavior of this function near the point (6, -2)? ? Using this information, on a separate sheet of paper sketch a possible contour diagram for f.
Consider the three points (2, 2), (4,4), and (6, -2). (a) Supposed that at (2, 2), we know that f = fy = 0 and fxx < 0, fyy = 0, and fry < 0. What can we conclude about the behavior of this function near the point (2, 2)? ? + (b) Supposed that at (4,4), we know that fa = fy = 0 and fax < 0, fyy > 0, and fry = 0. What can we conclude about the behavior of this function near the point (4,4)? ? + (c) Supposed that at (6, -2), we know that f = fy = 0 and fxx > 0, fyy < 0, and fry = 0. What can we conclude about the behavior of this function near the point (6, -2)? ? Using this information, on a separate sheet of paper sketch a possible contour diagram for f.
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:Consider the three points (2, 2), (4,4), and (6, —2).
(a) Supposed that at (2, 2), we know that fx = fy = 0 and ƒxx < 0, fyy =
= fy = 0 and fxx < 0, fyy = 0, and fxy < 0. What can we conclude about the behavior of this
function near the point (2, 2)? ?
0, and
and
(b) Supposed that at (4, 4), we know that fx = fy = 0 and fxx < 0, fyy > 0,
function near the point (4,4)? ?
fxy
fry = 0. What can we conclude about the behavior of this
(c) Supposed that at (6, -2), we know that fx = fy = 0 and fxx > 0, fyy < 0, and fxy = 0. What can we conclude about the behavior of
this function near the point (6, -2)? ?
Using this information, on a separate sheet of paper sketch a possible contour diagram for f.
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