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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dude wt is tht
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
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! >.<