Chapter 12.4, Problem 11E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 1-12, cost, revenue, and profit are in dollars and x is the number of units.The average cost of a product changes at the rate C ' ¯ ( x ) = − 6 x − 2 + 1 / 6 and the average cost of 10 units is $10.(a) Find the average cost function.(b) Find the average cost of 12 units. (a) To determine To calculate: The average cost function where the average cost of 6 units is$10 and the average cost of a product changes at a rate C¯(x)=6x2+16

Explanation

Given information:

The average cost of 6 units is $10 and The average cost of a product changes at a rate C¯(x)=6x2+16 Formula used: Average cost The integration of rate of change of average cost is defined as the average cost. C¯(x)=C¯(x)dx Integral formula, xndx=xn+1n+1+K Calculation: Consider the rate of change of average cost, C¯(x)=6x2+16 Now, use the formula, C¯(x)=C¯(x)dx And Substitute 6x2+16 for C¯(x) in above equation and evaluate C¯(x)=(6x2+16)dx Now, solve by the use of the integration formula (b) To determine To calculate: The average cost of 12 units where the average cost of 6 units is$10 and the average cost of a product changes at a rate C¯(x)=6x2+16

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