How to calculate minimum!

In above equation, put $x = y = z = k$

$\frac{x^4 + y^4 + z^4}{xyz} = \frac{k^4 + k ^4 + k^4}{(k)(k)(k)}$ $\frac{x^4 + y^4 + z^4}{xyz} = \frac{3k^4}{k^3} = 3k$

Now, as $k$ becomes smaller, value of above function becomes smaller and when $k \rightarrow 0$ , $min\bigg(\frac{x^4 + y^4 + z^4}{xyz}\bigg) = 3k \rightarrow 0$

Therefore,

$\color{#3D99F6}{\boxed{min\bigg(\frac{x^4 + y^4 + z^4}{xyz}\bigg) \rightarrow 0}}$

The minimum is 3???