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Suppose that the total cost function, in dollars, for the production of x units of a product is given by the equation shown below. C(x) = 13,230 + 40x + 0.3x2 Then the average cost of producing x items is represented by the following equation. (x) - total cost - 13,230 + 40 + 0.3x (a) Find the instantaneous rate of change of average cost with respect to the number of units produced, at any level of production. (b) Find the level of production at which this rate of change equals zero. (c) At the value found in part (b), find the instantaneous rate of change of cost and find the average cost. instantaneous rate of change of cost $ average cost $ What do you notice? O The instantaneous rate of change of cost is greater than the average cost. The instantaneous rate of change of cost equals the average cost. O The instantaneous rate of change of cost is less than the average cost.

Suppose that the total cost function, in dollars, for the production of x units of a product is given by the equation shown below. C(x) = 13,230 + 40x + 0.3x2 Then the average cost of producing x items is represented by the following equation. (x) - total cost - 13,230 + 40 + 0.3x (a) Find the instantaneous rate of change of average cost with respect to the number of units produced, at any level of production. (b) Find the level of production at which this rate of change equals zero. (c) At the value found in part (b), find the instantaneous rate of change of cost and find the average cost. instantaneous rate of change of cost $ average cost $ What do you notice? O The instantaneous rate of change of cost is greater than the average cost. The instantaneous rate of change of cost equals the average cost. O The instantaneous rate of change of cost is less than the average cost.

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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Suppose that the total cost function, in dollars, for the production of x units of a product is given by the equation shown below. C(x) = 13,230 + 40x + 0.3x? Then the average cost of producing x items is represented by the following equation. Cx) = total cost 13,230 %3D + 40 + 0.3x (a) Find the instantaneous rate of change of average cost with respect to the number of units produced, at any level of production. (b) Find the level of production at which this rate of change equals zero. x = (c) At the value found in part (b), find the instantaneous rate of change of cost and find the average cost. instantaneous rate of change of cost average cost What do you notice? O The instantaneous rate of change of cost is greater than the average cost. O The instantaneous rate of change of cost equals the average cost. O The instantaneous rate of change of cost is less than the average cost.
Transcribed Image Text:Suppose that the total cost function, in dollars, for the production of x units of a product is given by the equation shown below. C(x) = 13,230 + 40x + 0.3x? Then the average cost of producing x items is represented by the following equation. Cx) = total cost 13,230 %3D + 40 + 0.3x (a) Find the instantaneous rate of change of average cost with respect to the number of units produced, at any level of production. (b) Find the level of production at which this rate of change equals zero. x = (c) At the value found in part (b), find the instantaneous rate of change of cost and find the average cost. instantaneous rate of change of cost average cost What do you notice? O The instantaneous rate of change of cost is greater than the average cost. O The instantaneous rate of change of cost equals the average cost. O The instantaneous rate of change of cost is less than the average cost.
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