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.

Question

Mathematics

Barnes

26 September, 18:25

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.

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Autumn Evans · 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, ∞)