Prove: f:[0,oo)->[0,oo) that is concave and a>b>0. Then given a constant c>0 I claim that f(a+c)−f(a)<=f(b+c)−f(b).

Alberto Calhoun

Alberto Calhoun

Answered question

2022-11-08

Prove: f : [ 0 , ) [ 0 , ) that is concave and a > b > 0. Then given a constant c > 0 I claim that f ( a + c ) f ( a ) f ( b + c ) f ( b ).

Answer & Explanation

gortepap6yb

gortepap6yb

Beginner2022-11-09Added 19 answers

Hint: On one hand your inequality is same as f ( a + c ) f ( a ) c f ( b + c ) f ( b ) c and on second hand, if concave function have second derivative, then it is non-positive i.e. first derivative is not increasing.

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