For f(x) = (2x^2)+(8/x^2) when finding where y = 0 in the first derivative function, it doesn't exist?

The 1st derivative is f'(x) = 4x - 16^-3

and then I make it 0 = 4x - 16^-3

But there is no solution to that.

So what is it classified as because my question is asking me to find maximum/minimum and any points of inflexion

The 2nd derivative is f''(x) = 4 + 48^-4

But I can't go further because there is no solution to x?