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Homework Help: Functions extreminizer

  1. Jun 17, 2010 #1
    Let
    [tex]f(x):=\frac{1+(1+x)^{4}+(1-2x)^{4}}{\sqrt[4]{1+x^{4}}}[/tex]
    and [tex]x_{0}[/tex] be the minimizer of [tex]f(x)[/tex].
    Is it true that
    [tex]x_{0}[/tex] is the maximizer of
    [tex]g(x):=\frac{1+(1+x)(1+x_{0})^{3}+(1-2x)(1-2x_{0})^{3}}{\sqrt[4]{1+x^{4}}}?[/tex]

    Thanks in advance for any helpful answer.
     
  2. jcsd
  3. Jun 17, 2010 #2

    Mark44

    Staff: Mentor

    extreminizer?? I've never seen that word before.

    It's given that x0 is the minimizer of f, which means that f(x0) <= f(x) for all x in the domain of f.

    What can you say about g(x0)? You might want to compare f(x0) and g(x0).
     
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