the rate of change of total revenue with respect to the number of items sold at an instant. Solution Since marginal revenue is the rate of change of total revenue with respect to the number of units sold, we have Marginal Revenue (MR) = R dx = When x = , MR = ( ) + = Hence, the required marginal revenue is ` . EXERCISE . .
Find the rate of change of the area of a circle with respect to its radius r when (a) r = cm (b) r = cm . The volume of a cube is increasing at the rate of cm /s. How fast is the surface area increasing when the length of an edge is cm? .
The radius of a circle is increasing uniformly at the rate of cm/s. Find the rate at which the area of the circle is increasing when the radius is cm. . An edge of a variable cube is increasing at the rate of cm/s.
How fast is the volume of the cube increasing when the edge is cm long? . A stone is dropped into a quiet lake and waves move in circles at the speed of cm/s. At the instant when the radius of the circular wave is cm, how fast is the enclosed area increasing?
. The radius of a circle is increasing at the rate of . cm/s. What is the rate of increase of its circumference?
. The length x of a rectangle is decreasing at the rate of cm/minute and the width y is increasing at the rate of cm/minute. When x = 8cm and y = 6cm, find the rates of change of (a) the perimeter, and (b) the area of the rectangle. .
A balloon, which always remains spherical on inflation, is being inflated by pumping in cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is cm. .