9514 1404 393
Answer:
- -6: crosses
- 0: crosses
- 1: touches
- 4: crosses
Step-by-step explanation:
When the multiplicity is odd, the function changes sign on either side of the zero. Hence the graph crosses the x-axis.
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When the multiplicity is even, the function has the same sign on either side of the zero, so the graph only touches the x-axis, but does not cross.
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For the given zeros, the behavior is ...
-6, multiplicity odd, crosses the x-axis
0, multiplicity odd, crosses the x-axis (curve is flatter than at -6 or 4)
1, multiplicity is even, touches the x-axis
4, multiplicity is odd, crosses the x-axis
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Additional comment
The higher the multiplicity of the root, the "flatter" the curve is at the x-axis.
