Hello, classicstrings!
An interesting problem . . . I've never been asked to do this.
Sketch the square and comment on the number of turning points.
is a cubic with xintercepts: 6, 3, 4.
There are two turning points. Code:

 *

**  *
6 * *  *
  o  +  +  o  +  +  +  +  +  o   
* 3*  * 4
*  *
* * *
 **

has the same xintercepts but of order two.
. . The graph is tangent to the xaxis there.
Also the entire graph is above (or on) the xaxis. Code:

*  ** *
** * *
* * * * * *
* * * *  * *
  o* +  +  o* +  +  +  +  + *o   
6 3  4
There are five turnning points.