The area (in square units) of the triangle formed by the $X$-axis, the tangent and the normal drawn at $(1,1)$ to the curve $x^3+y^3=2 x y$ is

The value of the Rolle's theorem for the function $f(x)=2 \sin x+\sin 2 x$ in the interval $[0, \pi]$ is

If the function $y=g(x)$ representing the slopes of the tangents drawn to the curve $y=3 x^4-5 x^3-12 x^2+18 x+3$ is strictly increasing, then the domain of $g(x)$ is