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Suppose that $f$ is a twice differentiable function such that $$f(a) = 0,\, f(b) = 2,\, f(c) = − 1,\, f(d) = 2,\, f(e) = 0,$$ where $a < b < c < d < e$. What is the minimum number of zeroes of $g(x) = 2f'(x) + f''(x) f(x)$ in the interval $[a, e]$?

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Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the [homework] tag; people will still help, so don't worry. – Arturo Magidin May 13 '12 at 0:42
@ArturoMagidin We are no more using the homework tag – Kristoffer Ryhl Aug 1 '14 at 21:29

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