let f : be a monotonic function for which there exist a,b , c, d with a 0 , c 0 such that for all x the following equalities hold :

f(t)dt = ax+b and f(t)dt =cx+d.

Prove that f is a linear function , i.e, f(x)=mx+n for some m,n

Solution (AOPS) :

neelanjan wrote:

let f : be a monotonic function for which there exist a,b , c, d with a 0 , c 0 such that for all x the following equalities hold :

f(t)dt = ax+b and f(t)dt =cx+d.

Prove that f is a linear function , i.e, f(x)=mx+n for some m,n

f(t)dt = ax+b and f(t)dt =cx+d.

Prove that f is a linear function , i.e, f(x)=mx+n for some m,n

g(x)=a is diffrenablediffrenable

Diffrenable is lim ;

are period of

It is nonsense

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