TextBook Solutions for Punjab School Education Board Class 12 Mathematics Mathematics Part I Chapter 6 Application Of Derivatives

Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm   (b) r = 4 cm

Find the rate of change of the volume of a ball with respect to its radius r. How fast is the volume changing with respect to the radius when the radius is 2 m?

How fast is the volume of a ball changing with respect to its radius when the radius is 3 m?

A balloon which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the latter is 10 cm.

The cost function C(x), in rupees, of producing x items (x ≥ 15) in a certain factory is given by   Determine the marginal cost function and the marginal cost of producing 100 items. 

The total cost C(x) in Rupees,   associated with the production of x units of an item is given by C(x) = 0.005 x³ - 0.02 x² + 30 x + 5000.
Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

The total revenue in Rupees received from the sale of x units of a product is given by
                      R(x) = 13x² + 26x + 15.
Find the marginal revenue when x = 7.