$A$ stone is thrown vertically upwards from the top of a tower $64 \ m$ high according to the law $s=48t-16t^{2}$. The greatest height attained by the stone above the ground is (in $m$)

Find the points at which the function $f$ given by $f(x)=(x-2)^{4}(x+1)^{3}$ has
$(i)$ local maxima
$(ii)$ local minima
$(iii)$ point of inflexion

$A(1,15), B(3,-12), C(6,12)$ are three consecutive turning points of a continuous curve $y=f(x)$. If $f(x)=0$ only for $x=\alpha$ and $x=\beta$,then $|\beta-\alpha| < $

Among all sectors of a fixed perimeter,choose the one with maximum area. Then,the angle at the centre of this sector (i.e.,the angle between the bounding radii) is

If the petrol burnt in driving a motor boat varies as the cube of the velocity,then the speed (in $km/h$) of the boat relative to the water,going against a water flow of $C \ km/h$,so that the quantity of petrol burnt is minimum,is:

Local maximum and local minimum values respectively of the function $f(x)=(x-1)(x+2)^2$ are