Multiple Choice:
A point moves on the x-axis in such a way that its velocity at time t (t0) is given by v=lnt/t. At which value of t does v attain its maximum?
(A) 1
(B) e^(1/2)
(C) e
(D) e^(3/2)
(E) There is no maximum value for v.

Question

Multiple Choice:
A point moves on the x-axis in such a way that its velocity at time t (t>0) is given by v=lnt/t. At which value of t does v attain its maximum? 
(A) 1
(B) e^(1/2) 
(C) e
(D) e^(3/2)
(E) There is no maximum value for v.

dumbcow · Answer

dv/dt = (1-ln(t))/t^2
set equal to 0
1-ln(t) = 0
->ln(t) = 1
->t = e
Answer is C