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f-I-0-I-R-f-twice-derivable-f-f-continuous-f-x-f-x-f-x-2-x-I-then-prove-that-2f-x-y-2-f-x-f-y-x-y-I-

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Question Number 163209 by HongKing last updated on 04/Jan/22
f : I → (0 ; ∞) ; I ⊂ R f - twice derivable ; f^′ ; f^(′′) - continuous f^(′′) (x) f(x) ≥ (f^′ (x))^2 ; ∀ x ∈ I then prove that: 2f (((x + y)/2)) ≤ f(x) + f(y) ; ∀ x;y ∈ I
f:I→(0;∞);I⊂Rf−twicederivable;f′;f″−continuousf″(x)f(x)⩾(f′(x))2;∀x∈Ithenprovethat:2f(x+y2)⩽f(x)+f(y);∀x;y∈I

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