Please help me prove, that for all real $x,y,z$



Hint: It is three independent single-variable calculus problems. Do you know how to maximize $te^{-t^2}$?

  • $\begingroup$ Hm... need to use derivatives and calculate global maximum? I'll try $\endgroup$ – Steve Feb 26 '13 at 8:12
  • 1
    $\begingroup$ Derivative of $te^{-t^2}$ is $-2t^2e^{-t^2}+e^{-t^2}$. Set equal to $0$, solve. We get $t=1/\sqrt{2}$. So max is $\frac{1}{\sqrt{2}}e^{-1/2}$. Multiply by $3$. $\endgroup$ – André Nicolas Feb 26 '13 at 9:01
  • $\begingroup$ Thanks. I've solved this task :-) $\endgroup$ – Steve Feb 26 '13 at 9:26

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