Find extreme values of $f(x,y)=cos(x + y) + sin(x − y) + x^2$
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So, I get the following system of equations:
$-sin(x+y)+cos(x-y)+2x=0 \-sin(x+y)-cos(x-y)=0$
I got after a bit of simplification that either $ tan x =-1$ or $tan y=-1$, and that $|x|<=1$. But, I don't think this gives me a very nice' expression for the other variable in either case. Please can you verify if there are actually no "nice" solutions, or point out anything that I have done wrong. Thanks.
multivariable-calculus
edited Nov 15 at 22:40
Bernard
116k637108
asked Nov 15 at 22:35
Adienl
546316
add a comment |
up vote
0
down vote
favorite
So, I get the following system of equations:
$-sin(x+y)+cos(x-y)+2x=0 \-sin(x+y)-cos(x-y)=0$
I got after a bit of simplification that either $ tan x =-1$ or $tan y=-1$, and that $|x|<=1$. But, I don't think this gives me a very nice' expression for the other variable in either case. Please can you verify if there are actually no "nice" solutions, or point out anything that I have done wrong. Thanks.
multivariable-calculus
edited Nov 15 at 22:40
Bernard
116k637108
asked Nov 15 at 22:35
Adienl
546316
@Moo I am supposed to do this problem by hand, unfortunately.
– Adienl
Nov 15 at 22:53
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
So, I get the following system of equations:
$-sin(x+y)+cos(x-y)+2x=0 \-sin(x+y)-cos(x-y)=0$
I got after a bit of simplification that either $ tan x =-1$ or $tan y=-1$, and that $|x|<=1$. But, I don't think this gives me a very nice' expression for the other variable in either case. Please can you verify if there are actually no "nice" solutions, or point out anything that I have done wrong. Thanks.
multivariable-calculus
edited Nov 15 at 22:40
Bernard
116k637108
asked Nov 15 at 22:35
Adienl
546316
So, I get the following system of equations:
$-sin(x+y)+cos(x-y)+2x=0 \-sin(x+y)-cos(x-y)=0$
I got after a bit of simplification that either $ tan x =-1$ or $tan y=-1$, and that $|x|<=1$. But, I don't think this gives me a very nice' expression for the other variable in either case. Please can you verify if there are actually no "nice" solutions, or point out anything that I have done wrong. Thanks.
multivariable-calculus
multivariable-calculus
edited Nov 15 at 22:40
Bernard
116k637108
asked Nov 15 at 22:35
Adienl
546316
edited Nov 15 at 22:40
Bernard
116k637108
asked Nov 15 at 22:35
Adienl
546316
edited Nov 15 at 22:40
Bernard
116k637108
edited Nov 15 at 22:40
Bernard
116k637108
edited Nov 15 at 22:40
Bernard
116k637108
116k637108
asked Nov 15 at 22:35
Adienl
546316
asked Nov 15 at 22:35
Adienl
546316
asked Nov 15 at 22:35
Adienl
546316
546316
@Moo I am supposed to do this problem by hand, unfortunately.
– Adienl
Nov 15 at 22:53
add a comment |
@Moo I am supposed to do this problem by hand, unfortunately.
– Adienl
Nov 15 at 22:53
@Moo I am supposed to do this problem by hand, unfortunately.
– Adienl
Nov 15 at 22:53
@Moo I am supposed to do this problem by hand, unfortunately.
– Adienl
Nov 15 at 22:53
add a comment |
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@Moo I am supposed to do this problem by hand, unfortunately.
– Adienl
Nov 15 at 22:53