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Math Help - Functions and Combinatorics?

  1. #1
    Super Member fardeen_gen's Avatar
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    Functions and Combinatorics?

    Let S = \{1,2,3,\mbox{...}, 10\}. If m is the number of ways of selecting p and q from the set S such that the function f(x) = \frac{x^3}{3} + \frac{p}{2}x^2 + qx + 10 is a one-one function and n is the number of ways of selecting p and q from the set S such that |p - q| < 4, determine the greater of the two numbers.

    Answer:
    Spoiler:
    m = 62,\ n = 52


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  2. #2
    Junior Member
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    A function is one-to-one if and only if it is either strictly increasing or strictly decreasing.

    So take the derivative and see if you can work from there.
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