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5. What can be said about the signs of the partial derivatives fæ, fy, fax, and fyy when (x, y) corresponds to (a) a peak of f, (b) a depression of f, (c) a "saddle" point of f (looking like an actual saddle)? (Assume all of these partials exist there.) 6. Use the functions (a) f(x, y) = 9-x²-2y², (b) g(x, y) = 2x² + 3y² - 7, and (c) h(x, y) = 5x² - 7y² +3 and the origin (0, 0) to confirm your observations from the previous problem.

5. What can be said about the signs of the partial derivatives fæ, fy, fax, and fyy when (x, y) corresponds to (a) a peak of f, (b) a depression of f, (c) a "saddle" point of f (looking like an actual saddle)? (Assume all of these partials exist there.) 6. Use the functions (a) f(x, y) = 9-x²-2y², (b) g(x, y) = 2x² + 3y² - 7, and (c) h(x, y) = 5x² - 7y² +3 and the origin (0, 0) to confirm your observations from the previous problem.

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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5. What can be said about the signs of the partial derivatives fæ, fy, fax, and fyy when (x, y) corresponds to (a) a peak of f, (b) a depression of f, (c) a "saddle" point of f (looking like an actual saddle)? (Assume all of these partials exist there.) 6. Use the functions (a) f(x, y) = 9-x²-2y², (b) g(x, y) = 2x² + 3y² -7, and (c) h(x, y) = 5x² - 7y² +3 and the origin (0, 0) to confirm your observations from the previous problem.
Transcribed Image Text:5. What can be said about the signs of the partial derivatives fæ, fy, fax, and fyy when (x, y) corresponds to (a) a peak of f, (b) a depression of f, (c) a "saddle" point of f (looking like an actual saddle)? (Assume all of these partials exist there.) 6. Use the functions (a) f(x, y) = 9-x²-2y², (b) g(x, y) = 2x² + 3y² -7, and (c) h(x, y) = 5x² - 7y² +3 and the origin (0, 0) to confirm your observations from the previous problem.
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