May 23rd, 2017, 12:51 PM  #1 
Member Joined: Jan 2016 From: Blackpool Posts: 40 Thanks: 0  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. 
May 23rd, 2017, 01:27 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,778 Thanks: 2194 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.


Tags 
auxiliary, auxillary, equation 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Cartesian equation of loci from given complex equation  max233  Algebra  2  March 31st, 2017 09:40 PM 
Quadratic equation / Cubic equation  shaharhada  Algebra  2  August 30th, 2016 11:09 AM 
Equation jump in graphical algebra equation  DarkX132  Algebra  3  September 26th, 2014 10:15 PM 
Auxiliary discussion for "Advanced Analysis of Quintics"  JJacquelin  New Users  68  August 23rd, 2013 03:55 AM 
Show that an equation satisfies a differential equation  PhizKid  Differential Equations  0  February 24th, 2013 11:30 AM 