The demand for a certain product is represented by the function $p = 300 + 25x - x^2$ (in rupees), where x is the number of units demanded and p is the price per unit, then the marginal revenue when 15 units are sold, is

A car is moving along the curve $y = x^3 + 12$. The point(s) on the curve at which the rate of change of its y-coordinate at a certain time is 3 times the rate of change of its x-coordinate is/are

For the function $f(x) = -2x^3 + 3x^2 + 36x - 10$, which of the following is/are true?

(A) $f$ is increasing in $(-\infty, -2)$

(B) $f$ is increasing in $(-2, 3)$

(C) $f$ is decreasing in $(-\infty, -2)$

(D) $f$ is decreasing in $(3, \infty)$

Choose the correct answer from the options given below:

The appropriate change in the volume V of a cube of side $x$ metres caused by increasing the side by 2% is :

Function $f(x)=\sin3x, x \in \left[0,\frac{\pi}{2}\right]$ is decreasing in the interval

The sides of an equilateral triangle are increasing at the rate of 5 cm/sec. The rate at which the area increases when the side is 20 cm, is

The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is: