## If $g(x)=f(x)+f(1-x)$ and $f'(x) November 30

Let , $g(x)=f(x)+f(1-x)$ and $f'(x)<0$ for all $x\in (0,1)$. Then , $g$ is monotone increasing if (A) $(1/2,1)$.(B) $(0,1/2)$(C) $(0,1/2)\cup (1/2,1)$.(D) none.We have , $g'(x)=f'(x)-f'(1-x)$. Now $g'(x)>0$ if $f'(x)>f'(1-x)$. As $f'(x)<0$ so