Question

The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. Find the average value of the cost function over the interval [0, 700).

Answer 1

The average value of the cost function over the interval is of $23,500.

Explanation:

Average value of a function:

The average value of a function, over an inteval [a,b], is given by:

`A = (1)/(b-a) \int_(a)^(b) f(x) dx`

In this case:

Function
`C(x) = 20000 - 10x`, interval with
`a = 0,b = 700`

So

`A = (1)/(700) \int_(0)^(700) 20000+10x dx`

`A = (1)/(700) (20000x+5x^2)|_(0)^(700)`

So

`A = (20000(700)+5(700)^2)/(700) = 23500`

The average value of the cost function over the interval is of $23,500.