The acute angle between the curves $y=3 x^2-2 x-1$ and $y=x^3-1$ at their point of intersection which lies in the first quadrant is

If the rate of change of the slope of the tangent drawn to the curve $y=x^3-2 x^2+3 x-2$ at the point $(2,4)$ is $k$ times the rate of change of its abscissa, then $k=$

If $f(x)=x+\log \left(\frac{x-1}{x+1}\right)$ is a well-defined real valued function, then $f$ is

A real valued function $f(x)=\left|x^2-3 x+2\right|+2 x-3$ is defined on $[-2,1]$. If $m$ and $M$ are absolute minimum and absolute maximum values of $f$ respectively, then $M-4 m=$