The position of a particle is

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

s(t)=t^{3}-6kt^{2}+9k^{2}t

, where

k

is a positive constant and

t

is in seconds. The particle attains a local maximum position at

t=2\text{ s}

. What is the value of

k

? (a)

k=\dfrac{2}{3}

(b)

k=1

(c)

k=2

(d)

k=4