Is there a concave function that is positive and grows faster than this polynomial function as x goes to −oo?

Emmy Swanson

Emmy Swanson

Answered question

2022-10-25

Is there a concave function that is positive and grows faster than this polynomial function as x goes to ?

Answer & Explanation

Gael Irwin

Gael Irwin

Beginner2022-10-26Added 13 answers

There cannot be such a function. If f is positive and concave then for x < 1
0 < f ( x ) L ( x )
where L is the secant line joining ( 1 , f ( 1 ) ) and ( 0 , f ( 0 ) ), which means that f grows at most linear for x .

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