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 different interpretation of marginal cost Suppose a large
company makes 25,000 gadgets per year in batches of x items at a
time. After analyzing setup costs to produce each batch and taking
into account storage costs, planners have determined that the total
cost C(x) of producing 25,000 gadgets in batches of x items at a
time is given by a. Determine the marginal cost and average cost functions. Graph
and interpret these functions.
b. Determine the average cost and marginal cost when x = 5000.
c. The meaning of average cost and marginal cost here is different from earlier examples and exercises. Interpret the meaning
of your answer in part (b).
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