I'm supposed to find the maximum value of f(x,y)=xy if (x,y) is a point on the ellipse 9x^2+16y^2=144.

I have that y=lambda18x and x=lambda32y but I'm not sure how to go about solving for x and y.

Thanks :D

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- May 1st 2009, 10:19 AMjelloishLagrange Multipliers
I'm supposed to find the maximum value of f(x,y)=xy if (x,y) is a point on the ellipse 9x^2+16y^2=144.

I have that y=lambda18x and x=lambda32y but I'm not sure how to go about solving for x and y.

Thanks :D - May 1st 2009, 10:44 AMredsoxfan325
- May 1st 2009, 12:11 PMSpec
Another way to solve it is to switch to polar coordinates:

Then you just need to find the maximum of a function of one variable:

- May 1st 2009, 12:49 PMredsoxfan325