compare three values: 2^(1/2), 3^(1/3), 6^(16).

I know the function f(x)=x^(1/x) has max at x=e,

and lim f(x) = 0 when x-> 0,

lim f(x) = 1 when x-> OO

but how can we determine the relative value of f(x) when x=2, 3, 6?

compare three values: 2^(1/2), 3^(1/3), 6^(16).

I know the function f(x)=x^(1/x) has max at x=e,

and lim f(x) = 0 when x-> 0,

lim f(x) = 1 when x-> OO

but how can we determine the relative value of f(x) when x=2, 3, 6?

I know the function f(x)=x^(1/x) has max at x=e,

and lim f(x) = 0 when x-> 0,

lim f(x) = 1 when x-> OO

but how can we determine the relative value of f(x) when x=2, 3, 6?