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Suppose that a polynomial function p(x) crosses the horizontal line y=1 at exactly one point, crosses the horizontal line y=3 at exactly three points, and crosses the horizontal line y=5 at exactly five points (p is not tangent at any point to any of those three horizontal lines). What is the least possible degree of p?

 Nov 23, 2020
 #1
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I think it is 5

 Nov 24, 2020
 #2
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There are 7 turning points so p must be 8.

 Nov 24, 2020

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