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
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Originally Posted by jelloish 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 and So So you want to solve the system: The best thing to do is to get rid of first. So divide the first two equations to get: Substituting into the third equation gives us So the maximum of occurs when and , so the maximum value is
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:
Originally Posted by Spec 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: True. The derivative of is . Setting gives you . which is the same answer as above.
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