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Math Help - Maximum and minimum

  1. #1
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    Maximum and minimum

    Hi,

    Im doing a differentiation problem and somewhere i am going wrong so I am just going to type out my work and see if anyone can help

    Surface are of cylinder is 60cm and we need to find the maximum and minimum volume

    2pi r(h+r)=60
    h+r= 60/2pi r
    h+r=30/ pi r
    h= (30/pi r) -r
    h= (30-pi r^2)/ pi r)

    placing h into volume formula

    v= pi r^2*h

    substituting h leaves -pi r^3+30r

    dr/dv= -3r^2+30r=0
    3r(-r+10)
    r=10

    where do i go from here.

    how do i find the maximum and minimum??
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  2. #2
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    Quote Originally Posted by nikki1234 View Post
    substituting h leaves -pi r^3+30r

    dr/dv= -3r^2+30r=0
    Hi

    dv/dr = -3pi r^2+30
    the extrema are found when dv/dr=0 ==> r=sqrt(10/pi)
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  3. #3
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    Hi

    Yes Ive done that and ive got two answers. one being positive and one being negative. Im assuming the positive is the maximum volume. For the minimum do I try and find a solution nearest to 0 or do i differentiate again?
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  4. #4
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    For the minimum volume, you need first to determine the lowest and the highest possible value for r
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