The function $$f(x)=\log (1+x)-\frac{2 x}{2+x}$$ is increasing on

The coordinates of the point on the $$\sqrt{x}+\sqrt{y}=6$$ at which the tangent is equally inclined to the axes is

The function $$f(x)=4 \sin ^3 x-6 \sin ^2 x +12 \sin x+100$$ is strictly

The cost and revenue functions of a product are given by $$c(x)=20 x+4000$$ and $$R(x)=60 x+2000$$ respectively, where $$\mathrm{x}$$ is the number of items produced and sold. The value of $$x$$ to earn profit is