(D) e^(3/2)
v = ln(t) / t
max of v when dv/dt = 0
dv/dt = (t/t - ln(t))/t²
= [1 - ln(t)]/t² = 0
ln(t) = 1
t = e (option C)
check this is a max and not a min
d²v/dt² = [t²(-1/t) - 2t(1 - ln(t))]/t^4
= [-1 - 2t + 2t ln(t)]/t^4
= [-1 - 2e + 2e ln(e)]/e^4
= [-1 - 2e + 2e]/e^4
= -1/e^4 < 0 so it is a max
