How do you show that f(x,y)= x^4 + y^4 has a saddle point at (x,y) = (0,0)?

May 6, 2015

I don't believe it foes have a saddle point at $\left(0 , 0\right)$.

$f \left(0 , 0\right) = 0$ but for any other $\left(x , y\right)$, we have $f \left(x , y\right) > 0$.

It looks like $f$ has an absolute minimum at $\left(0 , 0\right)$.

May 6, 2015

I don't believe it does have a saddle point at $\left(0 , 0\right)$.

$f \left(0 , 0\right) = 0$ but for any other $\left(x , y\right)$, we have $f \left(x , y\right) > 0$.

It looks like $f$ has an absolute minimum at $\left(0 , 0\right)$.