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Math Help - partial derivative...

  1. #1
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    partial derivative...

    a)assume we have a cylinder ( with a top ) of height h and base radius r. if the top, bottom and wall costs per square meter are a, b and w dollars respectively, find the cost function K ( h, r, a, b, w )that gives the total material cost as a function of h, r, a, b, w
    b)find all 5 partial derivative of the function K

    how do i begin this question?
    surface area= 2 (pi)rh + 2(Pi)r^2

    top=a= (pi)r^2 bottom= b= (pi) r^2 wall=w=2(pi)r h
    dk/dr= 2(pi)h + 4(pi)r
    dk/dh= 2(pi)r

    TC= a(dk/dr)+ b(dk/dr) + w(dk/dr)(dk/dh) ?

    help please
    Last edited by KQ_jai; March 9th 2009 at 05:59 PM.
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  2. #2
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    Is this how its done?

    a)Total cost=apir^2 +bpir^2 +2wpirh
    \
    b)
    dk/dr= 2apir + 2bpir + 2wpih
    dk/dh=2wpir
    dk/da= pir^2
    dk/db= pir^2
    dk/dw=2pirh
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