Recent content by arcyqwerty

Well, that's as far as I got with my similar problem https://www.physicsforums.com/showthread.php?p=3582731&posted=1#post3582731" That might just be a max or something. Not entirely sure.

So... "A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S." Not quite sure what that means exactly, but perhaps its compact if there can be a finite subset of the points defined by the function? And... There seems to be two...

I'm not quite sure what you mean by compact or Weierstrass' Theorem but I think that the function is continuous

I think I'm working on something similar... this is what I would have done \begin{gathered} f\left( {x,y,z} \right) = {x^2}{y^2}{z^2};g\left( {x,y,z} \right) = {x^2} + {y^2} + {z^2} - 1 = 0 \\ \vec \nabla f = \left\langle {2x{y^2}{z^2},2{x^2}y{z^2},2{x^2}{y^2}z} \right\rangle ;\vec \nabla g...

Homework Statement Find max/min of x^2+y^2+z^2 given x^4+y^4+z^4=3Homework Equations Use of gradient vectors related by LaGrange MultiplierThe Attempt at a Solution \begin{gathered} f\left( {x,y,z} \right) = {x^2} + {y^2} + {z^2};g\left( {x,y,z} \right) = {x^4} + {y^4} + {z^4} - 3 = 0 \\...