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The DeWitt Company has found that the rate of change of its average cost for product is C'(x)=(1/4)-(100/x^2)where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00.(a) Find the average cost function for the product.(b) Find the average cost of 50 units of the product.

Question

The DeWitt Company has found that the rate of change of its average cost for product is C'(x)=(1/4)-(100/x^2)

where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00.

(a) Find the average cost function for the product.

(b) Find the average cost of 50 units of the product.

check_circleAnswer
Step 1

Given information:

The DeWitt Company has found that the rate of change of its average cost for product is  

1 100
C'(x)
4
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1 100 C'(x) 4

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Step 2

Calculation:

Integrate the function C\\\'(x) with respect to x, we get

 

 

T00
jC'(x)
4
1
C(x)x
100
+C
4
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T00 jC'(x) 4 1 C(x)x 100 +C 4

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Step 3

It is given that the average cost of producing 20 units ...

100
+C
C(x)
4
100
+C
(20)
C(20) (20)+
40 5+5+C
C 40-10
=30
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100 +C C(x) 4 100 +C (20) C(20) (20)+ 40 5+5+C C 40-10 =30

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Math

Calculus

Integration

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