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AP® Calculus AB-BC

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Difficult

Particle Speeding Up

APCALC-OZHGNI

The position of an object moving along a horizontal line is given by $s( t ) ={ \cfrac{1}{3} t }^{ 3 }-{ 3t }^{ 2 }+8t.$

Find all intervals on $t > 0$ where the object is speeding up.

A

$(3,\infty)$

B

$(4,\infty)$

C

$(0,2)\cup(4,\infty)$

D

$(2,3)\cup(4,\infty)$