(Solved): 316. It is a fact that the square root of 2 is the same as the fourth root of 4 -in other words, 2 ...

316. It is a fact that the square root of 2 is the same as the fourth root of 4 -in other words, $2^{1/2}=4^{1/4}$. Thus, the graph of $y=x^{1/x}$ goes through two points that have the same $y$-coordinate. As the diagram suggests, the maximum $y$-value for this curve occurs between $x=2$ and $x=4$. What is this $x$-value, to four places? 317. (Continuation) The diagram also suggests that the graph of $y=x^{1/x}$ has a horizontal asymptote. Investigate this possibility.