May 23rd, 2017, 01:51 PM  #1 
Member Joined: Jan 2016 From: Blackpool Posts: 77 Thanks: 2  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 05:16 PM. 
May 23rd, 2017, 02:27 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,118 Thanks: 2369 Math Focus: Mainly analysis and algebra 
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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auxiliary, auxillary, equation 
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