query: How to prove that e^x is convex?
positive_passages.docid: 142922
positive_passages.text: How to prove that $e^x$ is convex?
negative_passages.docid: 58410
negative_passages.text: Simplest or nicest proof that $1+x \le e^x$
negative_passages.docid: 54764
negative_passages.text: Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?
negative_passages.docid: 20626
negative_passages.text: Prove that $x^y < y^x$
negative_passages.docid: 139288
negative_passages.text: Formal proof that $e^x$ is not algebraic
negative_passages.docid: 66151
negative_passages.text: Solving inequality for convex functions.
negative_passages.docid: 113922
negative_passages.text: Proof that the intersection of any finite number of convex sets is a convex set
negative_passages.docid: 150727
negative_passages.text: Characterization convex function.
negative_passages.docid: 101690
negative_passages.text: Is linear function convex or concave?
negative_passages.docid: 36371
negative_passages.text: Exercise on convex functions
negative_passages.docid: 125175
negative_passages.text: convexity proof of a function including ln and sums
negative_passages.docid: 87567
negative_passages.text: How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
negative_passages.docid: 116387
negative_passages.text: How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
negative_passages.docid: 40403
negative_passages.text: Show that the function is convex
negative_passages.docid: 88328
negative_passages.text: Proof of $1+x\leq e^x$ for all x?
negative_passages.docid: 103367
negative_passages.text: Is inverse matrix convex?
negative_passages.docid: 40438
negative_passages.text: Proving that closed (and open) balls are convex