Describe where the function

is increasing, decreasing, concave, and convex. Sketch the graph of the function.

First we take the first and second derivatives,

Then we have the following,

This means that is increasing on and decreasing for .

Next, we have

This means that is concave on and convex for .

Finally, we sketch the function,

Hello

I guess that there is a problem with the plotted function . As log[1]=0 , the abciss scale is weird [ out of scale].

Yes it is distorted. Otherwise, it is not possible to see the concavity in the function – it looks like constant after x = e.