The engine in a boat has a power curve approximated by \[ y=-\frac{x^{2}}{10000}+\frac{33 x}{43}-26 \] where $x$ is the RPM and $y$ is the horsepower generated. At what RPM is the engine putting out maximum horsepower?. Round your answer to three decimal places. What is the maximum horsepower? Round your answer to three decimal places.

Step 1 ：The power curve of the engine is given by the equation \(y=-\frac{x^{2}}{10000}+\frac{33 x}{43}-26\), where \(x\) is the RPM and \(y\) is the horsepower generated.

Step 2 ：To find the RPM at which the engine is putting out maximum horsepower, we need to find the derivative of the given function and set it equal to zero.

Step 3 ：The derivative of the function is \(y' = \frac{33}{43} - \frac{x}{5000}\).

Step 4 ：Setting the derivative equal to zero gives us the critical points: \(0 = \frac{33}{43} - \frac{x}{5000}\). Solving for \(x\) gives us \(x = \frac{165000}{43}\).

Step 5 ：Rounding this to three decimal places, we find that the RPM at which the engine is putting out maximum horsepower is \(x = 3837.209\).

Step 6 ：Final Answer: The RPM at which the engine is putting out maximum horsepower is \(\boxed{3837.209}\).