$A$ ball is thrown in the air. Its height at any time $t$ is given by $h = 3 + 14t - 5t^2$. What is the maximum height it can reach?

If a running track of $500 \ ft$. is to be laid out enclosing a playground,the shape of which is a rectangle with a semicircle at each end,then the length of the rectangular portion such that the area of the rectangular portion is to be maximum is (in feet).

The adjacent sides of a rectangle with a given perimeter of $100 \, cm$ and enclosing the maximum area are:

$A$ cone of maximum volume is inscribed in a given sphere. Then the ratio of the height of the cone to the diameter of the sphere is:

Find the maximum and the minimum values,if any,of the function given by $f(x) = x, x \in (0, 1)$.

The maximum area of a rectangle that can be inscribed in a circle of radius $2 \text{ units}$ is