Question: Prove that the functions in (a)-(b) below are convex, without resorting to second derivatives. (a)f(x,y)=x2y for y>0 on RR++ (b)f(x)=log(1+ciaixi) on for (:1in}. (c) Using

Prove that the functions in (a)-(b) below are convex, without resorting to second derivatives.

(a)f(x,y)=x2y for y>0 on RR++

(b)f(x)=log(1+ciaixi) on for (:1in}.

(c) Using (b) show that det(x+Y)1ndet(x)1n+det(Y)1n for x,YinS++n.

Let f:RR++. Prove that f is log-convex if and only if earf(x) is convex for every cinR (we assume f is continuous but not that it is differentiable).

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