The radius of an air bubble is increasing at the rate of 0.5 centimetre per second. At what rate is the volume of the bubble increasing when the radius is 1 centimetre?

The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate if its area increasing when the side of the triangle is 20 cm?

For the curve, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when

The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue). If the total revenue (in rupees) received from the sale of x units of a product is given by R(x) =3x² +36x + 5, find the marginal revenue when x = 5, and write which value does the question indicate.

The length x, of a rectangle, is decreasing at the rate of 5 cm/minute and the width y, is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of the area of the rectangle.

The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?

The volume of a sphere is increasing at the rate of 3 cubic centimetre per second. Find the rate of increase of its surface area, when the radius is 2 cm.