Let f(x)= (ln x)/x for x>0. sketch the graph of y=f(x) indicating
asymptotes, regions where f is increasing, decreasing,convex, convave
,local extrema and points of inflection.  give absolute max and min
values on the interval {1,3}

Remember, you need to look at the first derivative to determine the
location of the maximum and/of minimum values.  These occur when the
first derivative is zero.  Also check values at the endpoints of the
interval.

Look at the second derivative to determine the points of inflection,
which occur when it is zero.  A negative second derivative indicates a
function that is concave downward and a positive second derivative
indicates a function that is concave upward.

To calculate a derivative of a quotient use the formula:

d/dx(u/v) = [v(du/dx) - u(dv/dx)] / v^2

f(x) = u/v = ln(x)/x

So  u = ln(x) and
    v = x

Here's a hint.  A well known constant may show up in the answer.