If the absolute maximum and absolute minimum values of the function $f(x)=x^3-2 x^2+x-3$ defined on $[0,2]$ are $M$ and $m$ respectively, then $M+m=$

If the slope of the tangent drawn at any point $(x, y)$ to the curve $y=f(x)$ is $3 x^2-5$ and $f(1)=2$, then the tangent at $(1,2)$ to the curve $y=f(x)$ intersects the curve at the point

The nearest approximate value of $\sqrt{2023}$ is (let $\Delta x=87$ ).

The slope of the normal drawn at a point $P$ to the curve $y=x^3-10 x^2+31 x-30$ is $-\frac{1}{14}$. If the co-ordinates of $P$ are integers, then the $X$-intercept of the tangent drawn at $P$ to the given curve is