Y=eˇx/(x+1)
(u/v)´= (u´v-uv´)/v²
u=eˇx, v=x+1, u´=eˇx , v´= 1
y´=(eˇx(x+1)-eˇx)/(x+1)²=(x.eˇx +eˇx -eˇx)/(x+1)²=x.eˇx/(x+1)²
a)bozpactaet: x∈(0,∞)
b)ybibaet: x∈x∈(-∞,0)
y´=0, ecli x=0
y´´=((eˇx+x)(x+1)²-2x.eˇx(x+1))/(x+1)ˇ4
y´´ (0)=((1+0).1²-2.0.eˇ0 (0+1)/(0+1)ˇ4=(1-0)/1=1
v točke x=0 minimum
y(0)=eˇ0/(0+1)=1/1=1
Minimum v točke A(0,1)
Maximum net.