Maximum and minimum function $f(x,y)=x$ on $\left\{ (x,y): x^4+y^4 = 4xy \right\} $ Determine minimum and maximum of function $f(x,y)=x$ on $\left\{ (x,y): x^4+y^4 = 4xy \right\} $.
I used Lagrange multiplier and received that 


*

*$f(3^{3/8},3^{1/8}) = 3^{3/8}$ is maximum

*$f(-3^{3/8},-3^{1/8}) = -3^{3/8}$ is maximum


Could you tell me is it correct?

In case you need a Mathematica code to do this kind of check in the future:
FindMinimum[{x,x^4+y^4==4x y},{x,0},{y,0}]
-3^{3/8}//N
FindMaximum[{x,x^4+y^4==4x y},{x,0},{y,0}]
3^{3/8}//N

Output:
{-1.5098,{x->-1.5098,y->-1.1472}}
{-1.5098}
{1.5098,{x->1.5098,y->1.1472}}
{1.5098}

You need a bit different code for Wolfram|Alpha:
min(x) when x^4+y^4==4x y, y is real

