Question: 5. We are looking for a theorem like this: Theorem. Let n and k be positive integers. Let f be a function defined on an
5. We are looking for a theorem like this: Theorem. Let n and k be positive integers. Let f be a function defined on an open interval I. Assume that f is n-times differentiable on I. IF f (n) has k zeroes on I, THEN f has at most ??zeroes on I. What is the smallest expression that you can write instead of ??that will make the theorem true? Your answer will depend on n and k. Once you think you know the answer, you need to do two things. First, prove that the theorem is true. Second, show with an example that your expression is the smallest that makes the theorem true.
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