The cost (in dollars) of producing x units of a certain commodity is c(x) = 9000 + 6x + 0.05x2. (a) find the average rate of change of c with respect to x when the production level is changed from x = 100 to the given value. (round your answers to the nearest cent.) (i) x = 102

The correct answer is $16.1 per unit.

Explanation:

C(x) = 9000 + 6x + 0.05x²

C(100) = 9000 + 6 × 100 + 0.05(100)²

           = 9000 + 600 + 500

            = 10,100

C(102) = 9000 + 6 × 102 + 0.05(102)²

           = 9000 + 612 + 520.5

            = 10,132.2

Now, the average rate of change of C with respect to x when production level changed from x = 100 to x = 102 is :

⇒

=

= $16.1 per unit

16

Explanation: Average rate of change of C with respect to X is given as

=

=

=

= 32/2

= 16

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