Consider the following. f(x, y) = x³ + y³ − 3x² + 6y² + 3x + 12y + 7 (a) Find the critical point. (x, y) = (b) Test for relative extrema. O The critical point is an absolute maximum. The critical point is an absolute minimum. The critical point is a saddle point. (c) List the critical points for which the Second Partials Test fails. (x, y) =
Consider the following. f(x, y) = x³ + y³ − 3x² + 6y² + 3x + 12y + 7 (a) Find the critical point. (x, y) = (b) Test for relative extrema. O The critical point is an absolute maximum. The critical point is an absolute minimum. The critical point is a saddle point. (c) List the critical points for which the Second Partials Test fails. (x, y) =
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 following.
f(x, y) = x³ + y³ − 3x² + 6y² + 3x + 12y + 7
(a) Find the critical point.
(x, y) =
(b) Test for relative extrema.
O The critical point is an absolute maximum.
The critical point is an absolute minimum.
The critical point is a saddle point.
(c) List the critical points for which the Second Partials Test fails.
(x, y) =
(d) Use a computer algebra system to graph the function.
-2
0
2
2
4 4
4
200
100
0
-100
-4
200
100
10
-100
-4
200
100
0
-100
200
100
0
-100
2
4
2
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