Dordt College Dr. Gary De Young's Website
Contents

Problem Set K

  1. Let f(x) be a real function on the real line with continuous third derivative. Prove that there exists a point a such that

    f(a)\cdot f^{\prime}(a)\cdot f^{\prime\prime}(a)\cdot f^{\prime\prime\prime}(a)\geq 0

  2. For each integer m, consider the polynomial

    P_m(x) = x^4 - (2m+4)x^2 + (m-2)^2
    For what values of m is P_m(x) the product of two non-constant polynomials with integer coefficients?
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