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Mathematics
Mathematics
Problem
The position of a particle is
s
(
t
)
=
−
t
3
+
3
k
t
2
+
12
t
s(t)=-t^{3}+3k t^{2}+12t
s
(
t
)
=
−
t
3
+
3
k
t
2
+
12
t
, where
k
k
k
is a positive constant and
t
≥
0
t\ge0
t
≥
0
. Determine the value of
k
k
k
such that the particle attains a local maximum position at
t
=
4
t=4
t
=
4
seconds.
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