Question

An object moves along the x-axis, its position at each time t> 0 given by X(t)= 1/4t^4- t^3 + t^2 Determine the time interval(s), if any, during which the object moves right.

Answer 1

X(t) = 1/4t^4 - t^3 + t^2
For the object to move right, X'(t) < 0
X'(t) = t^3 - 3t^2 + 2t < 0
t(t^2 - 3t + 2) < 0
t(t - 2)(t - 1) < 0
t > 0, t > 2, t < 1

Therefore, required interval is [0, 1] ∪ [2, ∞)