Saddle points on Lagrange Multipliers
$begingroup$
Suppose a function $f$ of two variables. To find the extremes of a function under certain conditions, I usually apply Lagrange multipliers.
For example,
Calculate the extremes of function $f(x,y)=-x^2+y^2-x$ in $left { (x,y) in mathbb{R}^2 : x^2+y^2 leq 1, yleq 0 right }$
What I would do is use the Lagrange method. And once I've applied it:
The absolute extremes would be those points whose image is superior.
With the remaining points, if they remain, calculate the Hessian to see if they are saddle points or local extremes.
Would it be well done?
multivariable-calculus lagrange-multiplier
asked Jan 16 at 16:28
user218559user218559
11
$endgroup$
add a comment |
$begingroup$
Suppose a function $f$ of two variables. To find the extremes of a function under certain conditions, I usually apply Lagrange multipliers.
For example,
Calculate the extremes of function $f(x,y)=-x^2+y^2-x$ in $left { (x,y) in mathbb{R}^2 : x^2+y^2 leq 1, yleq 0 right }$
What I would do is use the Lagrange method. And once I've applied it:
The absolute extremes would be those points whose image is superior.
With the remaining points, if they remain, calculate the Hessian to see if they are saddle points or local extremes.
Would it be well done?
multivariable-calculus lagrange-multiplier
asked Jan 16 at 16:28
user218559user218559
11
$endgroup$
add a comment |
$begingroup$
Suppose a function $f$ of two variables. To find the extremes of a function under certain conditions, I usually apply Lagrange multipliers.
For example,
Calculate the extremes of function $f(x,y)=-x^2+y^2-x$ in $left { (x,y) in mathbb{R}^2 : x^2+y^2 leq 1, yleq 0 right }$
What I would do is use the Lagrange method. And once I've applied it:
The absolute extremes would be those points whose image is superior.
With the remaining points, if they remain, calculate the Hessian to see if they are saddle points or local extremes.
Would it be well done?
multivariable-calculus lagrange-multiplier
asked Jan 16 at 16:28
user218559user218559
11
$endgroup$
Suppose a function $f$ of two variables. To find the extremes of a function under certain conditions, I usually apply Lagrange multipliers.
For example,
Calculate the extremes of function $f(x,y)=-x^2+y^2-x$ in $left { (x,y) in mathbb{R}^2 : x^2+y^2 leq 1, yleq 0 right }$
What I would do is use the Lagrange method. And once I've applied it:
The absolute extremes would be those points whose image is superior.
With the remaining points, if they remain, calculate the Hessian to see if they are saddle points or local extremes.
Would it be well done?
multivariable-calculus lagrange-multiplier
multivariable-calculus lagrange-multiplier
asked Jan 16 at 16:28
user218559user218559
11
asked Jan 16 at 16:28
user218559user218559
11
asked Jan 16 at 16:28
user218559user218559
11
asked Jan 16 at 16:28
user218559user218559
11
asked Jan 16 at 16:28
user218559user218559
11
11
add a comment |
add a comment |
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