Hello, Ahe!
Just "talk" your way through it . . .
Sketch a graph with the following characteristics:
(1) $\displaystyle f(\text{}2),\;f'(\text{}2),\text{ and }f''(\text{}2)$ are all negative.
(2) $\displaystyle f'(0)$ does not exist.
(3) $\displaystyle f(x)$ has a local maximum at (2,3).
(4) There is exactly one point of inflection on the interval (0,2).
(5) $\displaystyle \lim_{x\to\infty} f(x) \:=\:\text{}1$
(1) $\displaystyle f(\text{}2)$ is negative. .At $\displaystyle x = \text{}2$ the graph is below the xaxis.
. . .$\displaystyle f'(2)$ is negative. .The graph is decreasing.
. . .$\displaystyle f''(2)$ is negative. .The graph is concave down.
It is shaped like this: Code:
2
     +     
* :
* :
o
*
*
(2) $\displaystyle f'(0)$ does not exist.
. . .There is a vertical asymptote at $\displaystyle x=0.$
(3) There is a local maximum at (2,3)
(4) There is one inflection point on (0,2).
Since the curve is concave down at the maximum (2,3),
. . it was concave up to the left of the inflection point.
It looks something like this: Code:
 (2,3)
* o
 * : *
 * o : *
 * * :
 * :
++
0 2
(5) There is a horizontal asymptote: .$\displaystyle y \:=\:\text{}1$
I would guess that the graph looks like this: Code:

* o
 * : *
 * o : *
 * *: : *
 * : : *
2  : : *
++++*
:  1 2 *
     :    +                   
* :  y = 1
* : 
o 
* 
* 
* 

*
