An interesting problem . . . I've never been asked to do this.
is a cubic with x-intercepts: -6, -3, 4.
Sketch the square and comment on the number of turning points.
There are two turning points.
has the same x-intercepts but of order two.
** | *
-6 * * | *
- - o - + - + - o - + - + - + - + - + - o - - -
* -3* | * 4
* | *
* *| *
. . The graph is tangent to the x-axis there.
Also the entire graph is above (or on) the x-axis.
There are five turnning points.
* | ** *
** |* *
* * * *| * *
* * * * | * *
- - o*- + - + - o*- + - + - + - + - + -*o - - -
-6 -3 | 4