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How can I prove that a differentiable pseudoconvex function is also quasiconvex? Is it possible to do it simply using the definition of pseudoconvexity? Thanks.

Andrea
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    What have you tried already? Where did you get stuck? Questions with no context and no signs of effort are often poorly received on this site, and may be closed for those reasons. – postmortes Jan 17 '19 at 08:08
  • I apologize, I didn't want to break any of the site's rules, the problem is I don't know where to start actually. I tried using the definition of pseudoconvexity but I didn't get anywhere, then I tried to use the Taylor series of $f[(1-t)f(x)-tf(y)]$ trying to minimazing it using again the definition of pseudoconvexity but again nothing. I don't ask for a full execution, a hint for where to start or an idea of the proof is fine. Thank you. – Andrea Jan 17 '19 at 08:31
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    Does this ( https://math.stackexchange.com/questions/2007482/proof-of-first-order-condition-for-differentiable-quasiconvex-functions?rq=1 ) answer your question, by the way? – postmortes Jan 17 '19 at 09:47

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