- #1

thenewbosco

- 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

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- Thread starter thenewbosco
- Start date

- #1

thenewbosco

- 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

amcavoy

- 665

- 0

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

Are you sure you need Lagrange Multipliers for this?

- #3

thenewbosco

- 187

- 0

- #4

leon1127

- 486

- 0

thenewbosco said:

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

thenewbosco

- 187

- 0

I am sorry i still don't get it

- #6

leon1127

- 486

- 0

thenewbosco said:

I am sorry i still don't 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 doesn't 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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