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Lagrange multipliers

  • #1
187
0
Find the shortest and longest distance from the origin to the curve
[tex]x^2 + xy + y^2=16[/tex] and give a geometric interpretation...the hint given is to find the maximum of [tex]x^2+y^2[/tex]

i am not sure what to do for this problem

thanks
 

Answers and Replies

  • #2
665
0
thenewbosco said:
Find the shortest and longest distance from the origin to the curve
[tex]x^2 + xy + y^2=16[/tex] and give a geometric interpretation...the hint given is to find the maximum of [tex]x^2+y^2[/tex]

i am not sure what to do for this problem

thanks
Are you sure you need Lagrange Multipliers for this?
 
  • #3
187
0
it says for the hint to use the method of lagrange multipliers to find the maximum of [tex]x^2 + y^2[/tex] but i am not sure how to do it using any method, so any help is appreciated.
 
  • #4
486
0
thenewbosco said:
it says for the hint to use the method of lagrange multipliers to find the maximum of [tex]x^2 + y^2[/tex] but i am not sure how to do it using any method, so any help is appreciated.
Solve for y. use rate of change respect to the distance.
that is the "cal 1 method"

the path equation is constraint i think. apply Lagrange Multipliers on the distance formula
 
Last edited:
  • #5
187
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solve for y in what though. in the question it says [tex]x^2+y^2[/tex] this isnt even an equation though.
im sorry i still dont get it
 
  • #6
486
0
thenewbosco said:
solve for y in what though. in the question it says [tex]x^2+y^2[/tex] this isnt even an equation though.
im sorry i still dont get it
you can solve for y in tern of x
and then using the distance formula D = (y^2+x^2)^0.5
sub the y equation into the distance formula
take the first derivative
fine 0s
test it
done

that is cal 1 method, it requires a lot of work

[tex]x^2+y^2[/tex] looks really similar to the distance formula
[tex]D^2 = x^2 + y^2[/tex]

you can set [tex] D = f(x)[/tex] or [tex] D^2 = f(x)[/tex] and find the del of it, since the square doesnt where the extreme occurs, therefore the text tells you to fine the max of [tex]x^2+y^2[/tex]
 
Last edited:

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