Draw the graph of `y=(log_(e)x)^(2)`

Explanation

`y=(log_(e)x)^(2) gt 0` for all `x gt 0`
and when `x to 0, log_(e)x to -infty, therefore (log_(e)(x)^(2) to infty)`
When `x to infty, (log_(e)x)^(2) to infty`
Also for `(dy)/(dx) = 0, 2(log_(e)x)/(x)=0 rArr x=1`, which is clearly the point of minima `y(1)=1`
From these information, we can plot the graph of the function as shown in the following figure.

`y^('')=2(1-log_(e)x)/(x^(2))=0`
`y^('') lt 0` for `x gt e`
`y^('') gt 0` for `0 lt x lt e`