Step 1 :The problem is asking for the number of DVD/Blu-ray players produced when the marginal cost is $2626. This can be solved by setting the equation \(C=0.03 x^{2}-6 x+800\) equal to $2626 and solving for \(x\).
Step 2 :Solving the equation gives two solutions: -166.207938774685 and 366.207938774685.
Step 3 :However, the number of DVD/Blu-ray players produced cannot be negative. Therefore, the valid solution is 366.207938774685.
Step 4 :Rounding to the nearest whole number, the number of DVD/Blu-ray players produced when the marginal cost is $2626 is approximately \(\boxed{366}\).