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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.

Respuesta :

Answer:

Step-by-step explanation:

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

Slope = [tex]\frac{dc}{dx}[/tex]

Differentiating to get the slope;

[tex]\frac{dc}{dx}[/tex] = 4x - 24

Lowest cost is when the slope is zero, therfore ;

⇒ 4x-24 = 0

⇒ x = 6

substituting for x

c(6) = [tex]2(6)^{2}[/tex]-24(6)+720 = 648

Lowest cost is $648

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