If Water is poured into a cylindrical tank of radius 3.5 ft at the rate of $1 \mathrm{cu} \mathrm{ft} / \mathrm{min}$, then the rate at which the level of the water in the tank increases (in $\mathrm{ft} / \mathrm{min}$ ) is

$y=2 x^{3}-8 x^{2}+10 x-4$ is a function defined on [1,2]. If the tangent drawn at a point $(a, b)$ on the graph of this function is parallel to X-axis $a \in(1,2)$, then $a=$

If $m$ and $M$ are respectively the absolute minimum and absolute maximum values of a function $f(x)=2 x^{3}+9 x^{2}+12 x+1$ defined on $[-3,0]$, then $m+M=$

The maximum interval in which the slopes of the tangents drawn to the curve $y=x^{4}+5 x^{3}+9 x^{2}+6 x+2$ increase is