A farmer has collected data from one of his crops. Suppose the farmer found that the number of seeds, () S
(
t
)
, produced by a plant maturing at age
t
(in weeks) was
()=24
S
(
t
)
=
t
2
4
seeds per mature plant.
Further, the farmer discovered that only
()=11.76−24+3961.752+764.8
P
(
t
)
=
11.76
−
t
2
4
+
3961.75
t
2
+
764.8
t
plants matured to age
t
.
Determine the maximum rate of change of the crop's seed production. (answers rounded down)