Let $f(x)$ a positive decreasing real function with a positive domain. If $(1/f)$ is convex, is it true that $h(x)=xf(x)$ has a unique maximum?
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No, take $f(x) = \frac{1}{x}$ – fGDu94 Dec 12 '19 at 20:51
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What are the properties we need of $f(x)$ so $h(x)$ is strictly quasi-concave. – Quema Dec 12 '19 at 21:09