The amount A(t) of a certain item produced in a factory is given by

A(t) = 4000 + 48(t - 3) - 4(t - 3)³
where t is the number of hours of production since the beginning of the workday at 8:00 am. At what times is the rate of production increasing most rapidly?

1 answer

the rate of production would be A '(t)

this has a maximum when A ''(t) = 0

A '(t) = 48 - 12(t-3)^2
A ''(t) = -24(t-3

-24(t-3) = 0
t-3=0
t=3

look like 11:00 am