Question

The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x)=2x^(2)-24x+720, where x is the number of videos rented daily. Find the lowest cost to the nearest dollar.

Answer 1

Explanation:

C(x)=2x^(2)-24x+720

Slope =
`(dc)/(dx)`

Differentiating to get the slope;

`(dc)/(dx)` = 4x - 24

Lowest cost is when the slope is zero, therfore ;

⇒ 4x-24 = 0

⇒ x = 6

substituting for x

c(6) =
`2(6)^(2)`-24(6)+720 = 648

Lowest cost is $648