Suppose the total cost function, in dollars, for the production of x units of a product is given by C(x) = 4000 + 55x + 0.1x2. Then the average cost of producing x items is %3D total cost 4000 + 55 + 0.1x = (x)- (a) Find the instantaneous rate of change of average cost with respect to the number of units produced. That is to say, find C' (x). (b) Find the level of production at which this rate of change equals zero. In other words, solve the equation C' (x) = 0. (c) At the x value found in part (b), find the instantaneous rate of change of cost and find the axerage cost WWhat do you notice?

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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3. Suppose the total cost function, in dollars, for the production of x units of a product is
given by C(x) = 4000 + 55x + 0.1x². Then the average cost of producing x items is
C(x)
total cost
4000
+ 55 + 0.1x
(a) Find the instantaneous rate of change of average cost with respect to the number of
units produced. That is to say, find C'(x).
(b) Find the level of production at which this rate of change equals zero. In other words,
solve the equation C'(x) = 0.
(c) At the x value found in part (b), find the instantaneous rate of change of cost and find
the average cost. What do you notice?
Transcribed Image Text:3. Suppose the total cost function, in dollars, for the production of x units of a product is given by C(x) = 4000 + 55x + 0.1x². Then the average cost of producing x items is C(x) total cost 4000 + 55 + 0.1x (a) Find the instantaneous rate of change of average cost with respect to the number of units produced. That is to say, find C'(x). (b) Find the level of production at which this rate of change equals zero. In other words, solve the equation C'(x) = 0. (c) At the x value found in part (b), find the instantaneous rate of change of cost and find the average cost. What do you notice?
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