Question

the function f(x)=logx/x is increasing in

Answer 1

y=log x / x 
y'=(x/x - log x)/ x2
y'=0
0=1-log x
log x = 1
x=10 
dividing function in (-infinity , 10) and (10, infinity)
at ​(-infinity , 10)

let x=1
y' = 1 >0 
hence in this interval function is increasing 
similarly in interval ​(10, infinity)
let x = 100
y'<0 
hence function is decreasing