The distance traveled by a particle from a fixed point is given as s = (t\(^3\) - t\(^2\) - t + 5)cm. Find the minimum distance that the particle can cover from the fixed point?
A
2.3 cm
B
4.0 cm
C
5.2 cm
D
6.0 cm
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
S = t\(^3\) - t\(^2\) - t + 5
ds/dt = 3t\(^2\) - 2t - 1
As ds = 0
3t\(^2\) - 2t - 1 = 0
(3t+1)(t-1) = 0
∴ t = 1 or -1/3
At min pt t = 1
S = t\(^3\) - t\(^2\) - t + 5
put t = 1
= 1\(^3\) - \1(^2\) - 1 + 5
= 1 - 1 - 1 + 5
= 4
Source: Myschool Past Questions Archive (Record #9362)