Question

How would you sketch this curve y=(e^x)/(x)
finding zeros, max/mins, inflection points and asymptotes?

Answer 1

i was wondering how you would draw the other side of the graph, as i cant find any of the points thru 1st/2nd derivative

Answer 2

y'=e^x[(1/x)-(1/x^2)]=0 x=1 , y=e , y''=e^x[(1/x)-2(1/x^2)+2(1/x^3)] >0 for x=1
so (1,e) is min point(local) if x=0 then y=inf so x=0 (vertical) is asymptomatic line , if x=+inf then y=+inf ,
if x=-inf then y=0 so y=0 is asymptomatic line ( horizontal)
try to plot it is simple!

Answer 3

ive tried to plot it and i get a min at (1,e) but i dont know how the other part of the graph would look