Determine all critical points for the following function. \[ f(x)=x^{2}-256 \sqrt{x} \]

Step 1 ：Given the function \(f(x)=x^{2}-256 \sqrt{x}\), we need to find all the critical points.

Step 2 ：Critical points are where the derivative of the function is either zero or undefined.

Step 3 ：First, we find the derivative of the function: \(f'(x) = 2x - \frac{128}{\sqrt{x}}\).

Step 4 ：Next, we set the derivative equal to zero and solve for x to find the critical points: \(2x - \frac{128}{\sqrt{x}} = 0\). Solving this equation gives us the critical point \(x = 16\).

Step 5 ：We also need to check where the derivative is undefined. The derivative is undefined when the denominator of the fraction is zero, so we solve the equation \(\frac{128}{\sqrt{x}} = 0\). However, this equation has no solution.

Step 6 ：Final Answer: The critical points of the function \(f(x)=x^{2}-256 \sqrt{x}\) are \(\boxed{16}\).