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Math Help - Derivative word problem

  1. #1
    s3a
    s3a is offline
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    Derivative word problem

    Question:
    "The velocity of a wave of length L in deep water is

    v = K*sqrt(L/C + C/L)

    where K and C are known positive constants. What is the length of the wave that gives the minimum velocity?"

    Answer: L = C

    My work is attached (#43). (Page 10/14 of pdf file)

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
    Junior Member
    Joined
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    [quote=s3a;418838]Question:
    "The velocity of a wave of length L in deep water is

    v = K*sqrt(L/C + C/L)

    where K and C are known positive constants. What is the length of the wave that gives the minimum velocity?"

    Answer: L = C

    My work is attached (#43). (Page 10/14 of pdf file)

    -------------------------------------------------------------------

    hi, i havent looked at your work. but heres how i think it should go.

    aim: find when dv/dl=0, this will give min/max for v with respect to l.

    method:
    so differentiate v with respect to l;  dv/dl = k^2(1/c -1/c^2) and now find l when dv/dl=0.

    result:
    you will get something along the lines of l^2=c^2.

    conclusion:
    idk.
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