5) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Exercises for Section 3.3, #34) Let f (x, y) еба — ....

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Question

5) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Exercises for Section 3.3, #34) Let f (x, y) еба — . = 5ye

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Answer 1

Answer #1

$5 e$

a) First we find the critical points.

$41 5r 5r fx 05ye - 5e 0ye = e ye fy05e 16re e15 1x 0 4 5y0y e .y 1$

Hence $(0, 1$ is the critical point .

Loca maxima is $F(0, 1) 5-1-1 = 3$

b) Condition for existence of extremum at $(0, 1$ is

$f(0, 1)fy(0, 1) - (fy(0, 1))> 0$

$fr(0,1)5 fyy (0, 1)20 fry(0, 1) 5 . fr:(0, 1)fpy (0, 1) - (fay(0,1)) 5 x (-20) 25 125 <0$

Hence $f$ does not have a global maxima.

Answer 2

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