2) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Exercises for Section 3.3, # 34) Let f (x, y) = 5ye* - e5 -y5. (a) Show that f has a unique critical point and that this point is a local maximum for f. (b) Show that f is unbounded on the y-axis, and thus has no global maximum. (Note that for a differentiable function g (x) of a single variable, a unique critical point which is a local extremum is necessarily a global extremum. This example shows that this is not the case for functions of several variables.)
2) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Exercises for Section 3.3, # 34) Let f (x, y) = 5ye* - e5 -y5. (a) Show that f has a unique critical point and that this point is a local maximum for f. (b) Show that f is unbounded on the y-axis, and thus has no global maximum. (Note that for a differentiable function g (x) of a single variable, a unique critical point which is a local extremum is necessarily a global extremum. This example shows that this is not the case for functions of several variables.)
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Exercises for Section 3.3, # 34)
Let f (x, y) 5yeª – e5x – y5.
(a) Show that f has a unique critical point and that this point is a local maximum for f.
(b) Show that f is unbounded on the y-axis, and thus has no global maximum. (Note that for a differentiable function g (x) of a single variable, a unique
critical point which is a local extremum is necessarily a global extremum. This example shows that this is not the case for functions of several variables.)
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