Exercises 7 to 16: Find all critical points (if any) of a given function f (x, y) and determine whether they are local extreme points or saddle points. 7. f(x, y) = x² + y² + xy² 8. f(x, y) = x + y + xy 10. f(x, y) = x' + y° +3x²y – 3y x + y 9. f(x, y)= xy+ xy 11. f(x, y) = xye-x²-y² 12. f(x, y) = e* sin y 13. f(x, y) = x cos y 14. f(x, y) = In (x² + y² + 2) 15. f(x, y) = x sin (x + y) 16. f(x, y) = (x + y)(xy – 1) %3D %3D 17. Find the shortest distance from the point (2, 0, 3) to the plane x - y+ z = 4. 18. Find the shortest distance between the surface z = 1/xy and the origin. 19. Find the dimensions of a closed, rectangular box of given volume V > 0 that has minimuli surface area. 20. Find the point(s) on the surface xyz +1 -0 that are glonont
Exercises 7 to 16: Find all critical points (if any) of a given function f (x, y) and determine whether they are local extreme points or saddle points. 7. f(x, y) = x² + y² + xy² 8. f(x, y) = x + y + xy 10. f(x, y) = x' + y° +3x²y – 3y x + y 9. f(x, y)= xy+ xy 11. f(x, y) = xye-x²-y² 12. f(x, y) = e* sin y 13. f(x, y) = x cos y 14. f(x, y) = In (x² + y² + 2) 15. f(x, y) = x sin (x + y) 16. f(x, y) = (x + y)(xy – 1) %3D %3D 17. Find the shortest distance from the point (2, 0, 3) to the plane x - y+ z = 4. 18. Find the shortest distance between the surface z = 1/xy and the origin. 19. Find the dimensions of a closed, rectangular box of given volume V > 0 that has minimuli surface area. 20. Find the point(s) on the surface xyz +1 -0 that are glonont
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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I need help with numbers 9 and 14 please. Thank you!
Transcribed Image Text:Exercises 7 to 16: Find all critical points (if any) of a given function f (x, y) and determine whether
they are local extreme points or saddle points.
7. f(x, y) = x² + y² + xy²
8. f(x, y) = x + y +
xy
10. f(x, y) = x' + y° +3x²y – 3y
x + y
9. f(x, y)= xy+
xy
11. f(x, y) = xye-x²-y²
12. f(x, y) = e* sin y
13. f(x, y) = x cos y
14. f(x, y) = In (x² + y² + 2)
15. f(x, y) = x sin (x + y)
16. f(x, y) = (x + y)(xy – 1)
%3D
%3D
17. Find the shortest distance from the point (2, 0, 3) to the plane x - y+ z = 4.
18. Find the shortest distance between the surface z = 1/xy and the origin.
19. Find the dimensions of a closed, rectangular box of given volume V > 0 that has minimuli
surface area.
20. Find the point(s) on the surface xyz +1
-0 that are glonont
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