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

Step 1 ：The given derivative is $C^{\prime }(x)=4x^2-5x$. 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}