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.

Answer 1

dv/dt =
`(t* (1)/(t)-1*lnt )/( t^(2) ) = \\ = (1-+lnt)/(t^(2) )`
Velocity attains its maximum at dv/dt = 0, or:
1 - ln t = 0
ln t = 1

`log_(e)t= 1`
t = e
Answer: C)