Find all critical numbers for the function
$$f(x) = \frac{x^{1/3}}{x^2+3} - 3$$.
Give your answer as a comma separated list of numbers, arranged in increasing order. If there are no critical numbers, enter NONE.
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Classify each of the critical numbers you found above as a relative minimum (MIN), relative maximum (MAX), or neither (NEITHER). Again, give your answer as a comma separated list, in the same order that you listed the critical points above.
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List all numbers a such that the line $$x = a$$ is an asymptote for the graph of $$f$$. Give your answer as a comma separated list of numbers. If the graph has no vertical asymptotes, enter NONE.
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List all numbers b such that the line $$y = b$$ is an asymptote for the graph of $$f$$. If the graph has no horizontal asymptotes, enter NONE.
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