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 am. At what time is the rate of production increasing most rapidly?

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find double derivative and set equal to zero
solve

and make sure the first derivative is positive

48-12(t-3)^2 is the first dirivative?

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