Calculus: The derivative of this function x^3-8/3x^3 and the local extrema....

The chapter I'm studying is Connecting f1(first derivative) and f11 (second derivative) with the graph f.. Thank you in advance
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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.

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