How is the graph of \(\large x^{\frac{1}{x}}\) going to look like?

Calculus Level 3

\[\large 1, ~ 2^{\frac{1}{2}}, ~ 3^{\frac{1}{3}}, ~ 4^{\frac{1}{4}}, ~ 5^{\frac{1}{5}}, ~ 6^{\frac{1}{6}}, \cdots\]

Find the largest surd in the above series. Give your answer correct to three decimal places.

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