Let f: R R be a twice continuously differentiable function such that it has at...

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Let f: R → R be a twice continuously differentiable function such that it has at least 7 distinct zeros. Using the fact that ež f(x) has the same number of zeros as f(x), prove that f+4f' +4f" has at least 5 distinct zeros. Let f: R → R be a twice continuously differentiable function such that it has at least 7 distinct zeros. Using the fact that ež f(x) has the same number of zeros as f(x), prove that f+4f' +4f" has at least 5 distinct zeros.

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