Răspuns:
f(x)=lnx/x+lnx
X>0
a)lnx/(x+lnx)=lnx/lnx(x/lnx+1)=
1/(x/lnx+1)=1/∞=0 deoarece x/lnx→∞
b)f `(x)=[ln`x(x+lnx)-lnx(x+lnx) `](x+lnx)²=
[1/x(x+lnx)-lnx(1+1/x)]/(x+lnx)²=
(x/x+lnx/x-lnx-lnx/x)(x+lnx)²=
(1-lnx)/(x+lnx)²
c) f `(x)=0
1-lnx)/(x+lnx)²=0
1-lnx=0
lnx=1 x=e
(e,0) punct de extrem
Explicație pas cu pas:
