Hello, mathkid2007!
Graph the function $\displaystyle f(x)$ given the following characteristics:
$\displaystyle (1)\;f(0)= 4\text{ and }f(6)= 0$
$\displaystyle (2)\;f '(x)< 0 \text{ if }x< 2\text{ and }x> 4$
$\displaystyle (3)\;f '(2)\text{ does not exist and }f '(4)=0$
$\displaystyle (4)\;f '(x)>0\text{ if }2< x< 4$
$\displaystyle (5)\;f ''(x)< 0,\;x \neq 2$
(1) gives us two points: (0,4) and (6,0). Code:

4*



  +            *   
 6

(2) says the slope is negative for $\displaystyle x < 2$ and $\displaystyle x > 4.$ Code:


* 
4*
 * *
 * *
 * * 6
  +     +    +   *   
 2 4
 *

(3) says there is a vertical asymptote at $\displaystyle x = 2$
. . and a horizontal tangent at $\displaystyle x = 4.$ Code:
 x=2
*  :
4* :
 * : *
 * : : *
 * : : * 6
  +    +    +    *   
 *: 4
 : *
 *:
 :
(4) says the slope is positive on (2,4).
(5) says the graph is always concave down. Code:
 x=2
 :
*  :
4* :
 * : *
 * : * : *
 * : * : * 6
  +    + *   +    *   
 *:2 4
 :* *
 *:
 :
. . . There!