0
$\begingroup$

Is $\log x!-2\log (\frac{x}{2})!$ a decreasing or an increasing function?

How we can proof what type a function this is?

-Thanks in Advance!

  • 0
    Stirling should give $x\log x-x -2[\frac{x}{2}\log(\frac{x}{2})-\frac{x}{2}] = x\log 2$ which is increasing. – 2017-02-25
  • 0
    Thanks for your comment, I think I understood it with your comment and Mike's answer. – 2017-02-25

1 Answers 1

2

Your function can be rewritten as $\log\binom{x}{x/2}$. Does this help?

  • 0
    Since $\log\binom{x}{x/2}$ has a lower bound which is increasing... Thanks for your answer. – 2017-02-25
  • 0
    Whoah, that's absurd reasoning. A decreasing function can have a lower bound that is increasing. – 2017-02-25
  • 0
    @mathworker21 If a function is non decreasing and has a lower bound that is increasing, then can we say it's increasing? – 2017-02-26