Are all curves in the first quadrant that have the x and y axes for asymptotes convex when viewed from the origin? If not give an example. If yes, how can it be proved?
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No. Example: $$ f(x)=\frac{2+\sin x}{x},\quad x>0. $$
Julián Aguirre
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What condition can ensure that a curve with the x and y axes for asymptotes is convex? – phil342 Nov 01 '17 at 03:12
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There is no special condition for that kind of functions to be convex. – Julián Aguirre Nov 02 '17 at 16:35