What do you mean when you say "Fully analyze the graph"? Are you looking for the critical points, such as maximums/minimums, points of inflection, increasing/decreasing slopes, intervals of upward/downward concavity?

Question 12 is clear, so I'll do that for now until you specify what you need for 10.

h(x) = sqrt(lnx)

h'(x) = 1/2*1/sqrt(lnx)*1/x = 1/(2x*lnx)

h'(e) = 1/(2*e*lne) = 1/(2e)