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Math Help - inequality

  1. #1
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    inequality

    Find k>0 and m in so that (7n^3)+13n ≤ kn^3 for all integers n≥m
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  2. #2
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    Consider k=8
    The inequaliy simplifies to 13n<=n^3 This is true for all n>=3 Taking the derivative gives us 13 and 2n^2 which is enough to show that 13n will never catch up once the right hand side pulls ahead. If k is not restricted to integers any number greater than 7 will do though the m will change depending on which k you choose.
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