The formula for the total cost of producing an item is C=8x^2-176x+1800, where x is the number of units that the company makes. To minimize the cost of manufacturing, the company should produce a number of items. Determine this number. Solution We notice that the formula for the total cost is a function which is depending on the number of items manufactured. To find the minimum value for the cost, we have to differentiate the cost function. C\'(x) = (8x^2-176x+1800)\' C\'(x) = 16x - 176 From the theory, we know that a function has an extreme point, where it\'s first derivative is cancelling. C\'(x) = 0 16x - 176 = 0 16x=176 x=176/16 x=11 To verify if the point is a maximum or a minimum,we have to differentiate twice C(x). C\"(x) = (16x - 176)\' C\"(x) = 16>0 That means that any critical value will be a minimum. So, to minimize the cost, the number of items should be x=11..