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: $f^{\prime }(x)=2x-\frac{128}{\sqrt{x}}$.

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 $\boxed{{\displaystyle 16}}$.