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>=6 tangents for a point to y = (1 -x^2)^3 (II Soros Olympiad 1997-98 R3 11.4)

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June 6, 2024
algebraanalysiscalculus

Problem Statement

Consider the graph of the function y=(1āˆ’x2)3y = (1 -x^2)^3. Find the set of points M(x,y)M(x,y) through which you can draw at least 66 lines touching this graph.
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