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anonymous

  • 5 years ago

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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  1. anonymous
    • 5 years ago
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    find double derivative and set equal to zero solve

  2. anonymous
    • 5 years ago
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    and make sure the first derivative is positive

  3. anonymous
    • 5 years ago
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    48-12(t-3)^2 is the first dirivative?

  4. anonymous
    • 5 years ago
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    looks right to me

  5. anonymous
    • 5 years ago
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    when i got it equal to 0 i got t= 3

  6. anonymous
    • 5 years ago
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    from there i dont know

  7. anonymous
    • 5 years ago
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    you set the second derivative to zero -24(t - 3) = 0 t = 3

  8. anonymous
    • 5 years ago
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    yes, then what?

  9. anonymous
    • 5 years ago
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    it reaches the most rapid in 3 hours you start at 8 am plus 3 equal 11 am

  10. anonymous
    • 5 years ago
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    yo man you just blew my mind! thank you sooo much! now i know but can you explain a bit? why the 2nd derivative?

  11. anonymous
    • 5 years ago
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    sure the first derivative will give you the slope yes? if the slope is positive, then the rate at which it's being produced is increasing now here's the confusing part, so bare with me the second derivative will give you the slopes of the rate of production just like how when the first derivative hits zero, it's a max/min when the second derivative hits zero, it's when the rate of production is max/min so you solve for that make sense?

  12. anonymous
    • 5 years ago
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    i have to go now but if this doesn't make sense, i'll try coming on again later good luck!

  13. anonymous
    • 5 years ago
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    no it made perfecet sense! I just dont pay attention in class as much, ha! well ok thank you and have a good day!

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