Vinod Singh and Shweta Pawar Solutions for Chapter: Applications of Derivatives, Exercise 2: Critical Thinking

If the edge of a cube increases at the rate of $60 \mathrm{cm}$ per second, at what rate the volume is increasing when the edge is $90 \mathrm{cm}$

A running track of $440 \mathrm{ft}$ is to be laid out enclosing a football field, the shape of which is a rectangle with a semicircle at each end. If the area of rectangular portion is to be maximum, then lengths of sides are

A box is to be made from a sheet $12\times 12 \mathrm{sq}. \mathrm{cm}$, by cutting equal squares from the four corners and turning up its sides. Find the length of the side of the square to be cut out, in order to obtain a box of the largest possible volume?

The maximum height is reached in $5$ seconds by a stone thrown vertically upwards and moving under the equation $10s=10ut-49t^2$, where $s$ is in metre and $t$ is in second. The value of $u$ is

A man of height $2 \mathrm{m}$ walks directly away from a lamp of height $5 \mathrm{m}$ on a level road at $3 \mathrm{m}/\mathrm{s}$. The rate at which the length of his shadow is increasing is

A square plate is contracting at the uniform rate of $2 {\mathrm{cm}}^2/\sec$. The rate at which the perimeter is decreasing when the side of the square is $16 \mathrm{cm}$ long is

If $A+B=\frac{\pi }{2}$, the maximum value of $\cos A\cos B$ is

If $f\left(x\right)$ satisfies the conditions for Rolle's theorem on $\left[3, 5\right]$, then${\int }_3^{5}f\left(x\right)dx$ equals