, where satisfies the relation and . Then is equal…

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Functions · Functions

Problem

y=f(x)

, where

f

satisfies the relation

f(x+y)=2f(x)+x f(y)+y\sqrt{f(x)}\ \forall x,y\in\mathbb{R}

and

f'(0)=0

. Then

f(6)

is equal to