The interval in which the function $f(x) = x^3$ increases less rapidly than $g(x) = 6x^2 + 15x + 5$ is:

Let $x$ and $y$ be the sides of two squares such that $y = x - x^2$. The rate of change of the area of the second square with respect to the area of the first square is

$A$ street light is at the top of a $12 \ m$ pole. $A$ man $2 \ m$ tall walks away from the pole towards a wall $12 \ m$ away from the pole at a speed of $1/2 \ m/s$. The rate at which his shadow on the wall is decreasing when he is $8 \ m$ from the wall is:

The rate of change of the volume of a sphere with respect to its surface area,when its radius is $2 \text{ cm}$,is

$A$ particle moves along the curve $y = x^2 + 2x$. At what point on the curve do the $x$ and $y$ coordinates of the particle change at the same rate?

The volume of a sphere is increasing at the rate of $4 \pi \text{ cm}^3/\text{sec}$. When its volume is $288 \pi \text{ cm}^3$, the rate of increase (in $\text{cm/sec}$) in its radius is