The maximum value of 
31
[ (
1)
1]
x x −
+
, 0
1
≤x
≤  is
(A)
1
3
31


(B) 1
2
(C) 1
(D) 0
Miscellaneous Examples
Example 30 A car starts from a point P at time t = 0 seconds and stops at point Q The
distance x, in metres, covered by it, in t seconds is given by
x
t
t
=
−


2 2
3
Find the time taken by it to reach Q and also find distance between P and Q Solution Let v be the velocity of the car at t seconds Now
x =
2 2
t3
t 

−




Therefore
v = dx
dt  = 4t – t2 = t(4 – t)
Thus, v = 0 gives t = 0 and/or t = 4