For the following exercises, the cost of producing x cellphones is described by the function C(x) = x2 − 4x + 1000. Find the average rate of change in the total cost as x changes from x = 10 to x = 15.

For the following exercises, the cost of producing x cellphones is described by the function C(x) = x2 − 4x + 1000.

Find the average rate of change in the total cost as x changes from x = 10 to x = 15.

Solutions

Expert Solution

The average rate of change (AROC) between two points {a, f(a)} and {a + h, f(a + h)} is given by:

AROC = {f(a + h) – f(a)}/h

Consider the cost of producing x cell phones is as follows:

C(x) = x2 – 4x + 1000

Determine the average rate in change of total cost as x changes from x = 10 to x = 15 as follows:

{C(15) – R(10)}/[(15 – 10) = (15)2 – 4 × 15 + 1000 – {(10)2 – 4 × 10 +1000}]/(15 – 10)

= {225 – 60 + 1000 – (100 – 40 + 1000)}/5

= {225 – 60 + 1000 – 100 + 40 – 1000}/5

= (265 – 160)/5

Further simplify:

{C(15) – R(10)}/(15 – 10) = 105/5

= 21

Junaid answered 1 year ago

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