A linear cost function is C(x) = 9x + 650. (Assume C is measured in dollars.) (a) What are the slope and the C-intercept? slope C-intercept (b) What is the marginal cost MC? MC = What does the marginal cost mean? O Each additional unit produced reduces the cost by this much (in dollars). O If production is increased by this many units, the cost increases by $1. O If production is increased by this many units, the cost decreases by $1. O Each additional unit produced costs this much (in dollars). (c) What are the fixed costs? (d) How are your answers to parts (a), (b), and (c) related? O slope = fixed costs, and C-intercept = marginal cost O slope = marginal cost, and C-intercept = fixed costs slope = marginal cost C-intercept C-intercept = marginal cost slope (e) What is the cost of producing one more item if 50 are currently being produced? What is the cost of producing one more item if 100 are currently being 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.
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