Find the minimum value of
\[x^2 + 8x + \frac{64}{x^3}\]for $x > 0.$
Question:
Find the minimum value of
\[x^2 + 8x + \frac{64}{x^3}\]for $x > 0.$
Answer:
Let's think step by step.

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Find the minimum value of
\[x^2 + 8x + \frac{64}{x^3}\]for $x > 0.$
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