A researcher at a textbook manufacturing company finds that the revenue is given byR(x)=5x2−40x.What is the marginal revenue at x=20, and what does it mean?Select the correct answer below:The marginal revenue is $40, which means that revenue increases by $40 for each additional textbook produced.The marginal revenue is $160, which means that revenue is $1,600 when 10 textbooks are produced.The marginal revenue is $160, which means that when 20 textbooks are produced, the revenue increases by $160 for each additional textbook produced.The marginal revenue is $40, which means that revenue is shrinking at the rate of $40 per textbook produced.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
A researcher at a textbook manufacturing company finds that the revenue is given by
R(x)=5x2−40x.
What is the marginal revenue at x=20, and what does it mean?
Select the correct answer below:
The marginal revenue is $40, which means that revenue increases by $40 for each additional textbook produced.
The marginal revenue is $160, which means that revenue is $1,600 when 10 textbooks are produced.
The marginal revenue is $160, which means that when 20 textbooks are produced, the revenue increases by $160 for each additional textbook produced.
The marginal revenue is $40, which means that revenue is shrinking at the rate of $40 per textbook produced.
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