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<ol><li>Consider the real polynomial p(x) = x3 − x in a real variable x. Find all x such

that p(x) = 0.</li><li>Again, consider the same p(x) with x real. For which real values y are there three real solutions to p(x) = y? You might want to sketch the graph.</li><li>When is the real derivative p′(x) = 0?</li><li>What is the behavior of p(x) for real values of x near the real locations where p′(x) = 0?</li></ol>

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x = 0, x =-1, x =1 x = 0, x =-1, x =1 [Graph is at explanation... View the full answer

graph px.png

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