If f(x)=(x3-8)/3x3=⅓-(8/3)x-3.
The derivative is f'(x)=8/x4 which can never be zero, so there are no relative (local) extrema. The absolute maximum is infinity and the absolute minimum is negative infinity. So there are no defined absolutes. f(x)=⅓ is the horizontal asymptote, and the vertical axis is the vertical asymptote.