READ AND UNDERSTAND Point of Diminishing Returns If a company decides to increase spending on advertising, it expects sales to increase. At first, sales will increase at an increasing rate and then increase at decreasing rate. The dollar amount π₯ at which the rate of change of sales goes from increasing to decreasing is called the point of diminishing returns. This is also the amount at which the rate of change has a maximum value. Money spent beyond this amount may increase sales but at a lower rate. A T-shirt manufacturer is planning to expand its workforce. It estimates that the number of T-shirts produced by hiring π₯new workers is given by
(A) When is the rate of change of T-shirt production increasing and when is it decreasing?
(B) What is the point of diminishing returns and the maximum rate of change of T-shirt production?
(C) Write a brief interpretation of this result using the read and understand part.
READ AND UNDERSTAND Point of Diminishing Returns If a company decides to increase spending on advertising, it expects sales to increase. At first, sales will increase at an increasing rate and then increase at decreasing rate. The dollar amount π₯ at which the rate of change of sales goes from increasing to decreasing is called the point of diminishing returns. This is also the amount at which the rate of change has a maximum value. Money spent beyond this amount may increase sales but at a lower rate. A T-shirt manufacturer is planning to expand its workforce. It estimates that the number of T-shirts produced by hiring π₯new workers is given by
(A) When is the rate of change of T-shirt production increasing and when is it decreasing?
(B) What is the point of diminishing returns and the maximum rate of change of T-shirt production?
(C) Write a brief interpretation of this result using the read and understand part.
is decreasing at the rate of 
, what is the rate of change in the radius of circle? Is it increasing or decreasing?
, and the height of the cylinder is increasing at a rate of 
. At a certain instant, the base radius is 
and the height is 
. What is the rate of change of the volume of the cylinder at the instant?
