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Do Lagrange's multipliers fail in this case?
Lagrange multipliers - maximum and minimum values given constraintExplain Lagrange multipliers?Lagrange Multipliers to determine min and maxLagrange Multipliers: Find $min$ of $f(x,y)=3(x+1) +2(y-1)$ subject to the constraint $x^2+y^2=4$Finding minimum using Lagrange multipliersHow to use the Lagrange Multipliers to find the min and max of this function?Using Lagrange multipliers to find max and min values?Why am I allowed to assume x or y are equal to 0 in this Lagrange multipliers problem?Issues with the “standard” intuition behind Lagrange MultipliersMaximize a bivariate function under constraints by Lagrange multipliers
$begingroup$
Question:
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)
f(x,y)= y^2 - x^2 and (1/4)x^2 + y^2 = 9
I've tried solving it like I would all other questions of this type, but I get λ=4 which doesn't seem right. Am I doing something wrong or is it a DNE situation?
lagrange-multiplier
edited yesterday
Bernard
122k741116
asked yesterday
SarahSarah
11
New contributor
Sarah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
|
show 1 more comment
$begingroup$
Question:
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)
f(x,y)= y^2 - x^2 and (1/4)x^2 + y^2 = 9
I've tried solving it like I would all other questions of this type, but I get λ=4 which doesn't seem right. Am I doing something wrong or is it a DNE situation?
lagrange-multiplier
edited yesterday
Bernard
122k741116
asked yesterday
SarahSarah
11
New contributor
Sarah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
I get, when I solve the Lagrange equations, $x=0$ (and $lambda=1$) or $y=0$ (and $lambda=4$). Then there's a max at $x=0, y=pm 3$ and a min at $y=0, x=pm 6$.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician Isn´t $lambda_2=colorred-4$ If we change $9$ to $9.01$ the minimum changes from $-36$ to $-36+(-4cdot 0.01)=-36.04$
$endgroup$
– callculus
yesterday
$begingroup$
@ancientmathematician Yes, I can comprehend that. But wouldn´t be then $lambda_1$ negative if $lambda_2=4$?
$endgroup$
– callculus
yesterday
$begingroup$
@callculus, you are right of course.Sorry.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician There is no excuse needed. I was just wondering. Thanks for the replies.
$endgroup$
– callculus
yesterday
|
show 1 more comment
$begingroup$
Question:
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)
f(x,y)= y^2 - x^2 and (1/4)x^2 + y^2 = 9
I've tried solving it like I would all other questions of this type, but I get λ=4 which doesn't seem right. Am I doing something wrong or is it a DNE situation?
lagrange-multiplier
edited yesterday
Bernard
122k741116
asked yesterday
SarahSarah
11
New contributor
Sarah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Question:
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)
f(x,y)= y^2 - x^2 and (1/4)x^2 + y^2 = 9
I've tried solving it like I would all other questions of this type, but I get λ=4 which doesn't seem right. Am I doing something wrong or is it a DNE situation?
lagrange-multiplier
lagrange-multiplier
edited yesterday
Bernard
122k741116
asked yesterday
SarahSarah
11
New contributor
Sarah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Bernard
122k741116
asked yesterday
SarahSarah
11
New contributor
Sarah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Bernard
122k741116
edited yesterday
Bernard
122k741116
edited yesterday
Bernard
122k741116
122k741116
asked yesterday
SarahSarah
11
New contributor
Sarah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
SarahSarah
11
asked yesterday
SarahSarah
11
11
New contributor
Sarah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Sarah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Sarah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
I get, when I solve the Lagrange equations, $x=0$ (and $lambda=1$) or $y=0$ (and $lambda=4$). Then there's a max at $x=0, y=pm 3$ and a min at $y=0, x=pm 6$.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician Isn´t $lambda_2=colorred-4$ If we change $9$ to $9.01$ the minimum changes from $-36$ to $-36+(-4cdot 0.01)=-36.04$
$endgroup$
– callculus
yesterday
$begingroup$
@ancientmathematician Yes, I can comprehend that. But wouldn´t be then $lambda_1$ negative if $lambda_2=4$?
$endgroup$
– callculus
yesterday
$begingroup$
@callculus, you are right of course.Sorry.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician There is no excuse needed. I was just wondering. Thanks for the replies.
$endgroup$
– callculus
yesterday
|
show 1 more comment
1
$begingroup$
I get, when I solve the Lagrange equations, $x=0$ (and $lambda=1$) or $y=0$ (and $lambda=4$). Then there's a max at $x=0, y=pm 3$ and a min at $y=0, x=pm 6$.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician Isn´t $lambda_2=colorred-4$ If we change $9$ to $9.01$ the minimum changes from $-36$ to $-36+(-4cdot 0.01)=-36.04$
$endgroup$
– callculus
yesterday
$begingroup$
@ancientmathematician Yes, I can comprehend that. But wouldn´t be then $lambda_1$ negative if $lambda_2=4$?
$endgroup$
– callculus
yesterday
$begingroup$
@callculus, you are right of course.Sorry.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician There is no excuse needed. I was just wondering. Thanks for the replies.
$endgroup$
– callculus
yesterday
1
1
$begingroup$
I get, when I solve the Lagrange equations, $x=0$ (and $lambda=1$) or $y=0$ (and $lambda=4$). Then there's a max at $x=0, y=pm 3$ and a min at $y=0, x=pm 6$.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
I get, when I solve the Lagrange equations, $x=0$ (and $lambda=1$) or $y=0$ (and $lambda=4$). Then there's a max at $x=0, y=pm 3$ and a min at $y=0, x=pm 6$.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician Isn´t $lambda_2=colorred-4$ If we change $9$ to $9.01$ the minimum changes from $-36$ to $-36+(-4cdot 0.01)=-36.04$
$endgroup$
– callculus
yesterday
$begingroup$
@ancientmathematician Isn´t $lambda_2=colorred-4$ If we change $9$ to $9.01$ the minimum changes from $-36$ to $-36+(-4cdot 0.01)=-36.04$
$endgroup$
– callculus
yesterday
$begingroup$
@ancientmathematician Yes, I can comprehend that. But wouldn´t be then $lambda_1$ negative if $lambda_2=4$?
$endgroup$
– callculus
yesterday
$begingroup$
@ancientmathematician Yes, I can comprehend that. But wouldn´t be then $lambda_1$ negative if $lambda_2=4$?
$endgroup$
– callculus
yesterday
$begingroup$
@callculus, you are right of course.Sorry.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@callculus, you are right of course.Sorry.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician There is no excuse needed. I was just wondering. Thanks for the replies.
$endgroup$
– callculus
yesterday
$begingroup$
@ancientmathematician There is no excuse needed. I was just wondering. Thanks for the replies.
$endgroup$
– callculus
yesterday
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
Hint: Use $$y^2=9-frac14x^2$$ and you will get a Problem in only one variable:$$f(x,pmsqrt9-frac14x^2)=9-frac14x^2-x^2$$
answered yesterday
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Hint: Use $$y^2=9-frac14x^2$$ and you will get a Problem in only one variable:$$f(x,pmsqrt9-frac14x^2)=9-frac14x^2-x^2$$
answered yesterday
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
$endgroup$
add a comment |
$begingroup$
Hint: Use $$y^2=9-frac14x^2$$ and you will get a Problem in only one variable:$$f(x,pmsqrt9-frac14x^2)=9-frac14x^2-x^2$$
answered yesterday
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
$endgroup$
add a comment |
$begingroup$
Hint: Use $$y^2=9-frac14x^2$$ and you will get a Problem in only one variable:$$f(x,pmsqrt9-frac14x^2)=9-frac14x^2-x^2$$
answered yesterday
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
$endgroup$
Hint: Use $$y^2=9-frac14x^2$$ and you will get a Problem in only one variable:$$f(x,pmsqrt9-frac14x^2)=9-frac14x^2-x^2$$
answered yesterday
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
answered yesterday
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
answered yesterday
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
answered yesterday
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.4k42866
77.4k42866
add a comment |
add a comment |
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1
$begingroup$
I get, when I solve the Lagrange equations, $x=0$ (and $lambda=1$) or $y=0$ (and $lambda=4$). Then there's a max at $x=0, y=pm 3$ and a min at $y=0, x=pm 6$.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician Isn´t $lambda_2=colorred-4$ If we change $9$ to $9.01$ the minimum changes from $-36$ to $-36+(-4cdot 0.01)=-36.04$
$endgroup$
– callculus
yesterday
$begingroup$
@ancientmathematician Yes, I can comprehend that. But wouldn´t be then $lambda_1$ negative if $lambda_2=4$?
$endgroup$
– callculus
yesterday
$begingroup$
@callculus, you are right of course.Sorry.
$endgroup$
– ancientmathematician
yesterday
$begingroup$
@ancientmathematician There is no excuse needed. I was just wondering. Thanks for the replies.
$endgroup$
– callculus
yesterday