Find the average rate of change (in $ per unit) 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.)

Question

The cost (in dollars) of producing x units

 of a certain commodity is C(x) = 8,000 + 12x + 0.15x².

(a)

Find the average rate of change (in $ per unit) 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=

(ii)

x =

$ per unit

(b)

Find the instantaneous rate of change (in $ per unit) of C with respect to x when x = 100.

 (This is called the marginal cost.)

$   per unit

Answer 1

You haven't given a "given value".

Let's assume that x is increased from 100 units to 102 units.

Then average rate of change = (C(102) - C(100)) / (102 - 100)

Instantaneous rate of change when x = 100 is C'(100).

C'(x) = 12 + 0.30x

So, C'(100) = 12 + 30 = $42 / unit.