Find the particular antiderivative of the following derivative that satisfies the given condition.
\[
C^{\prime}(x)=4 x^{2}-5 x ; C(0)=2,000
\]

Step 1 ：The given derivative is \(C^{\prime}(x)=4 x^{2}-5 x\). To find the antiderivative, we integrate \(C^{\prime}(x)\) with respect to \(x\).

Step 2 ：The antiderivative of \(C^{\prime}(x)\) is given by \(C(x) = \int C^{\prime}(x) dx = \int (4x^2 - 5x) dx\).

Step 3 ：Using the power rule for integration, we get \(C(x) = \frac{4}{3}x^3 - \frac{5}{2}x^2 + C\), where \(C\) is the constant of integration.

Step 4 ：We are given that \(C(0) = 2000\). Substituting these values into the equation, we get \(2000 = \frac{4}{3}(0)^3 - \frac{5}{2}(0)^2 + C\).

Step 5 ：Solving for \(C\), we get \(C = 2000\).

Step 6 ：Therefore, the particular antiderivative of \(C^{\prime}(x)\) that satisfies the given condition is \(C(x) = \frac{4}{3}x^3 - \frac{5}{2}x^2 + 2000\).

Step 7 ：\boxed{C(x) = \frac{4}{3}x^3 - \frac{5}{2}x^2 + 2000}