G. t. a. part one
Web19 Likes, 0 Comments - No.9 (@no9artenviro) on Instagram: "#PillarsofChange is a public art project for everyone of all ages and abilities who want to engag..." Web(a) f′′(x) ≤ 0 for x ≥ 0. (b) Since t2/2 is convex we have t2/2 ≥ x2/2+x(t−x) = xt−x2/2. This is the general inequality g(t) ≥ g(x)+g′(x)(t−x), which holds for any differentiable convex function, applied to g(t) = t2/2. Another (easier?) way to establish t2/2 ≤ −x2/2+xt is to note that t2/2+x2/2−xt = (1/2)(x−t)2 ≥ 0. Now just move x2/2−xt to the other side.
G. t. a. part one
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