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 time is the rate of production increasing most rapidly?

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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 time is the rate of production increasing most rapidly?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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dude wt is tht
ummmmmmmmmmmmm
i forgot is production=cost-revnue or something liek that?

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oh well wats tht 2 tht yhu said dude
of wait im retard just forget about what I said i think i was thinking or profit lol
besides we are given the production function so taking the derivative will give us the rate of production
set A''(t) = 0 That will get you the highest production rate. -24t+72 = 0 t=3 8AM + 3Hours = 11AM
So the double derivative gives the highest production rate?
no to find max and min you find the first derivative
first derivative is the rate of production, second derivative is the (rate of rate) of production, If you want to find the Maximum production you set first derivative =0 If you want to find the Maximum RATE of production you set second derivative =0
yes elouis is right second rate of rate
Ahh thanks for clarifying that! I missed something like that on a practice AP test! >.<
i gave you a medal elouis lol
haha Thank you! i to you too.

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