lagrange multipliers

thenewbosco

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

amcavoy

Are you sure you need Lagrange Multipliers for this?

thenewbosco

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.

leon1127

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

thenewbosco

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

leon1127

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]