Question Number 102234 by Harasanemanabrandah last updated on 07/Jul/20
Answered by OlafThorendsen last updated on 07/Jul/20
![f(x) = x−elnx, x>0 f′(x) = 1−(e/x) f′(x) = 0 ⇔ x = e f(e) = e−elne = e−e = 0 And for x∈]e;+∞[ f′(x)>0 Then f(π) > 0 ⇔ π−elnπ>0 ⇔ π>elnπ ⇔ πlne>elnπ ⇔ lne^π >lnπ^e ⇔ e^π >π^e](Q102236.png)