Given a function f(x) on R, and that f(x) is strictly increasing and strictly concave: f'(x) > 0, and f''(x) <0. Is it always true that, for such function, we have: f(a+b) < f(a) + f(b) a,b are real numbers.

Jamie Medina

Jamie Medina

Answered question

2022-11-24

Given a function f ( x ) on R, and that f ( x ) is strictly increasing and strictly concave: f ( x ) > 0, and f ( x ) < 0. Is it always true that, for such function, we have:
f ( a + b ) < f ( a ) + f ( b )
a , b are real numbers.

Answer & Explanation

Cale Terry

Cale Terry

Beginner2022-11-25Added 10 answers

No. Consider f ( x ) = e x . Then e t = f ( 0 + t ) is not smaller than f ( 0 ) + f ( t ) = 1 e t .

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