Question

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?

Answer 1

dude wt is tht

Answer 2

ummmmmmmmmmmmm

Answer 3

i forgot is production=cost-revnue or something liek that?

Answer 4

oh well wats tht 2 tht yhu said dude

Answer 5

of wait im retard just forget about what I said i think i was thinking or profit lol

Answer 6

besides we are given the production function
so taking the derivative will give us the rate of production

Answer 7

set A''(t) = 0
That will get you the highest production rate.
-24t+72 = 0
t=3
8AM + 3Hours = 11AM

Answer 8

So the double derivative gives the highest production rate?

Answer 9

no to find max and min you find the first derivative

Answer 10

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

Answer 11

yes elouis is right second rate of rate

Answer 12

Ahh thanks for clarifying that! I missed something like that on a practice AP test! >.<

Answer 13

i gave you a medal elouis lol

Answer 14

haha Thank you! i to you too.