- #1

- 187

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[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

- Thread starter thenewbosco
- Start date

- #1

- 187

- 0

[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

- #2

- 665

- 0

Are you sure you need Lagrange Multipliers for this?thenewbosco said:

[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

- #3

- 187

- 0

- #4

- 486

- 0

Solve for y. use rate of change respect to the distance.thenewbosco said:

that is the "cal 1 method"

the path equation is constraint i think. apply Lagrange Multipliers on the distance formula

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- #5

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im sorry i still dont get it

- #6

- 486

- 0

you can solve for y in tern of xthenewbosco said:

im sorry i still dont get it

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]

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