query: Proving that the tangent to a convex function is always below the function
positive_passages.docid: 151981
positive_passages.text: Tangent line of a convex function
negative_passages.docid: 141529
negative_passages.text: Proving existence of a minimum
negative_passages.docid: 53132
negative_passages.text: A convex subset of a set has 'smaller' boundary than the set?
negative_passages.docid: 55866
negative_passages.text: Convex + Monotone =? Convex
negative_passages.docid: 64836
negative_passages.text: Functions that are always less than their derivatives
negative_passages.docid: 60521
negative_passages.text: Continuity of a convex function
negative_passages.docid: 57514
negative_passages.text: The Minkowski sum of two convex sets is convex
negative_passages.docid: 138457
negative_passages.text: Seminorms: Absolute Convexity
negative_passages.docid: 115495
negative_passages.text: Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
negative_passages.docid: 86518
negative_passages.text: Does $X$ have a lower bound?
negative_passages.docid: 57943
negative_passages.text: If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
negative_passages.docid: 15924
negative_passages.text: Convexity and strong lower semicontinuity imply weak lower semicontinuity
negative_passages.docid: 158399
negative_passages.text: Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
negative_passages.docid: 597
negative_passages.text: f is differentiable on convex domain D and Re(f')>0 implies f is injective on D
negative_passages.docid: 25738
negative_passages.text: Jensen's Inequality implies convexity?
negative_passages.docid: 115930
negative_passages.text: Is every convex function on an open interval continuous?
negative_passages.docid: 18763
negative_passages.text: injective holomorphic function on a convex set