Assume that it costs a company approximately C(x) - 800,000 + 340x + 0.0005x2 dollars to manufacture x game systems in an hour. (a) Find the marginal cost function C'(x). C'(x) = Use it to estimate how fast the cost is increasing when x = 60,000. per game system Compare this with the exact cost of producing the 60,001st game system. The cost is increasing at the rate of $ per game system. The exact cost of producing the 60,001st game system is $ . The actual cost producing the 60,001st game system is .Select-.. e the estimated cost of producing the 60,001st game system found using the marginal cost function. (b) Find the average cost function C(x) and the average cost to produce the first 60,000 game systems. (Round your answer to the nearest cent.) Cx) = C(60,000) -$ (c) Using your answers parts (a) and (b), determine whether the average cost is rising or falling at production level of 60,000 game systems. The marginal cost from (a) is Select- the average cost from (b). This means that the average cost is Select- e at a production level of 60,000 game systems.
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.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
