Is $h:xto expleft[-frac{x^2}{2}right]left(expleft[frac{x^4}{24n}right]-1right)$ increasing?
3
$begingroup$
I struggling to show this function ins increasing on $mathbb{R}^+$ $$h:xto expleft[-dfrac{x^2}{2}right]left(expleft[dfrac{x^4}{24n}right]-1right) qquad nin mathbb{N}^*$$ With the derivative I've found $$h'(x)=xe^{-frac{x^2}{2}}left[left(dfrac{x^2}{6n}-1right)e^{frac{x^4}{24n}}+1right]$$ $h'(x)ge 0iff left(dfrac{x^2}{6n}-1right)e^{frac{x^4}{24n}}+1ge 0$ and now I'm blocked...
real-analysis
share | cite | improve this question
edited Dec 2 '18 at 12:43
Stu
asked Dec 2 '18 at 12
