The given function represents the position of a particle traveling along a horizontal line. s(t) = 2t^3 - 3t^2 - 12t + 2 for t ? 0 (a) Find the velocity and acceleration functions. v(t) = a(t) = (b) Determine the time intervals when the object is slowing down or speeding up. (Enter your answers using interval notation.) slowing down speeding up
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The velocity function is the first derivative of the position function, \( s(t) \). Given \( s(t) = 2t^3 - 3t^2 - 12t + 4 \), differentiate each term with respect to \( t \): \[ v(t) = \frac{d}{dt}(2t^3) - \frac{d}{dt}(3t^2) - \frac{d}{dt}(12t) + \frac{d}{dt}(4) Show moreā¦
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