The position of a particle is

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

s(t)=-t^{3}+3k t^{2}+12t

, where

k

is a positive constant and

t\ge0

. Determine the value of

k

such that the particle attains a local maximum position at

t=4

seconds.