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May 23rd, 2017, 12:51 PM   #1
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Auxiliary equation

What is the minimum value of yx^3 on the circle x^2 + y^2 = 4?

I started by using the auxiliary equation to get two expressions for the partial derivatives of x and y and got for y: 0 = (x^3) - 2λy
x: 0 = (3x^2) - 2λy

I am having trouble now cancelling out either the x or y term and was wondering if someone could help, thanks!

Last edited by skipjack; May 23rd, 2017 at 04:16 PM.
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May 23rd, 2017, 01:27 PM   #2
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I would parametrise the circle in terms of a single variable $t$ and then find the extrema of $y(t)x^3(t)$, a function of $t$ only.
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