JEE Advanced 2012 Mathematics question
Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p'(0) is
Answer: 9
Solution
p' must vanish at 1 and 3, so the least-degree choice is (a cubic p). For a maximum at 1 and minimum at 3, p' changes from + to − at 1, so k > 0. Then
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