The total weekly cost (in dollars) incurred by a company in pressing $x$ compact discs is $C(x)=4,000+3 x-0.0001 x^{2}, 0 \leq x \leq 6,000$.
Round answers to the nearest cent.
What is the actual cost incurred in producing the $2,001^{\text {st }}$ disc?
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Step 1 ：The cost function given, \(C(x)=4,000+3 x-0.0001 x^{2}\), is a cumulative cost function. It gives the total cost of producing x discs.

Step 2 ：To find the cost of producing the 2001st disc, we need to find the difference between the cost of producing 2001 discs and the cost of producing 2000 discs.

Step 3 ：First, calculate the cost of producing 2001 discs: \(C(2001)=4,000+3(2001)-0.0001(2001)^{2} = 9602.5999\).

Step 4 ：Next, calculate the cost of producing 2000 discs: \(C(2000)=4,000+3(2000)-0.0001(2000)^{2} = 9600.0\).

Step 5 ：Subtract the cost of producing 2000 discs from the cost of producing 2001 discs to find the cost of the 2001st disc: \(9602.5999 - 9600.0 = 2.599899999999252\).

Step 6 ：Round this value to the nearest cent to get the final answer: \(\boxed{2.60}\).