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AP® Calculus AB-BC

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Moderate

Higher Order Derivatives: Particle Motion

APCALC-1BNFNO

A particle moves along a line such that its position can be modeled by $s\left( t \right) =2{ t }^{ 3 }-12{ t }^{ 2 }+18t-3$ for $t\ge 0$.

Over which of the following intervals is the acceleration always negative?

A

$\left( 0,\infty \right) $

B

$\left( 0,2 \right) $

C

$\left( 1,3 \right) $

D

$\left( 2,\infty \right) $