Let f in C^2 (i.e, f is differentiable twice and f′,f′′ are continuous. Show that f can be written as f(x)=g(x)+h(x) where g(x) is convex for any x and h(x) is concave for any x.

Adrian Brown 2022-11-20 Answered
Let f C 2 (i.e, f is differentiable twice and f , f are continuous. Show that f can be written as f ( x ) = g ( x ) + h ( x ) where g ( x ) is convex for any x and h ( x ) is concave for any x.
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Answers (1)

Camden Stanton
Answered 2022-11-21 Author has 14 answers
Write f as the sum of a (not necessarily continuous) non-negative function and non-positive function. Then integrate twice.
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