$\"\"$

The condition are :

$\"\"$

I/D test :

If $\"\"$ on the interval, then $\"\"$ is increasing on the interval.

If $\"\"$ on the interval, then $\"\"$ is decreasing on the interval.

Concavity test :

If $\"\"$ for all $\"\"$ in the interval, then the graph of $\"\"$ is concave upward on the interval.

If $\"\"$ for all $\"\"$ in the interval, then the graph of $\"\"$ is concave downward on the interval.

Graph :

Graph the function such that all the conditions are satisfied :

Using above tests,

$\"\"$ represents that $\"\"$ is increasing on $\"\"$ .

$\"\"$ represents that $\"\"$ is decreasing on $\"\"$ .

The critical point is $\"\"$ .

Therefore it has a either local maximum or minimum at the critical point.

$\"\"$ represents that there is a vertical asymptote at $\"\"$ .

$\"\"$ represents that $\"\"$ is concave upward on $\"\"$ . $\"\"$

$\"\"$

Graph the function is drawn such that all the conditions are satisfied is

$\"\"$