Find dL/dx set to zero. Solve for x.
(27+x)/x * sqrt(64+x^2)

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  1. What a nasty function to differentiate!
    I wrote it as

    L = [(27+x)√(64+x^2)]/x

    used a combination of quotient rule and product rule and got an answer of

    dL/dx = (x^3-1728)/[(x^2)(√(64+x^2)]

    setting this to zero gives only one real result:
    x^3 = 1728
    x = 12

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