Determine the critical points of the function f(r, y) = 4x +4y + x²y+ xy? and whether they are local maxima, local minima, or saddle points. %3D 6.Setthe derivatives to 0. 02.10. 24+2xy+ 4+x +2xy3D →-4-x²-2xy=0 0. 4+2xy+y -0 S=x²=y=±x_ %3D -4-2xy-x²=0 2-0 तखु नशि * If y=-x then fx=0 4+2xy+y=Q 2 P164+2x1-x) +l-xl=06 4-2x2+x²-0 xel 니-X=0 H=x² x=#2] E 2. →If y=x then f=0 4+2xy+u=Q6 xyty 2=D0 4+2x1xx)²= 0 2-0 4+2x²+x²= 0 4+3x%=D0 3=-4 (No Real Solutions

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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please help me, I'm having a difficult time in finding the critical points:

F(x) = 4 + 2xy + y^2

F(y) = 4 + x^2 + 2xy

F(xx) = 2y

F(yy) = 2x

F(xy) = 2x + 2y

Determine the critical points of the function
f(r, y) = 4x +4y + x²y+ xy?
and whether they are local maxima, local minima, or saddle points.
%3D
Transcribed Image Text:Determine the critical points of the function f(r, y) = 4x +4y + x²y+ xy? and whether they are local maxima, local minima, or saddle points. %3D
6.Setthe derivatives to 0.
02.10.
24+2xy+
4+x
+2xy3D
→-4-x²-2xy=0
0.
4+2xy+y -0
S=x²=y=±x_
%3D
-4-2xy-x²=0
2-0
तखु नशि
* If y=-x then fx=0 4+2xy+y=Q 2
P164+2x1-x) +l-xl=06
4-2x2+x²-0
xel 니-X=0
H=x²
x=#2] E
2.
→If y=x then f=0 4+2xy+u=Q6
xyty
2=D0
4+2x1xx)²= 0
2-0
4+2x²+x²= 0
4+3x%=D0
3=-4 (No
Real
Solutions
Transcribed Image Text:6.Setthe derivatives to 0. 02.10. 24+2xy+ 4+x +2xy3D →-4-x²-2xy=0 0. 4+2xy+y -0 S=x²=y=±x_ %3D -4-2xy-x²=0 2-0 तखु नशि * If y=-x then fx=0 4+2xy+y=Q 2 P164+2x1-x) +l-xl=06 4-2x2+x²-0 xel 니-X=0 H=x² x=#2] E 2. →If y=x then f=0 4+2xy+u=Q6 xyty 2=D0 4+2x1xx)²= 0 2-0 4+2x²+x²= 0 4+3x%=D0 3=-4 (No Real Solutions
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