Find the absolute extrema if they exist, as well as all values of $x$ where they occur. \[ f(x)=-x^{4}+4 x^{3}-4 x^{2}+1 \]

Step 1 ：First, we need to find the critical points of the function. Critical points occur where the derivative of the function is zero or undefined. So, we need to find the derivative of the function and set it equal to zero to find the critical points.

Step 2 ：The derivative of the function \(f(x) = -x^{4} + 4x^{3} - 4x^{2} + 1\) is \(f'(x) = -4x^{3} + 12x^{2} - 8x\).

Step 3 ：Setting the derivative equal to zero gives us the critical points: \(x = 0, 1, 2\).

Step 4 ：Now that we have the critical points, we need to evaluate the function at these points as well as at the endpoints of the domain to find the absolute extrema. The domain of the function is all real numbers, so there are no endpoints to consider. We just need to evaluate the function at the critical points.

Step 5 ：Evaluating the function at the critical points gives us the function values: \(f(0) = 1, f(1) = 0, f(2) = 1\).

Step 6 ：The absolute maximum of the function is 1 and it occurs at \(x = 0\) and \(x = 2\). The absolute minimum of the function is 0 and it occurs at \(x = 1\).

Step 7 ：Final Answer: The absolute maximum of \(f(x)\) is \(\boxed{1}\) and it occurs at \(x = 0\) and \(x = 2\). The absolute minimum of \(f(x)\) is \(\boxed{0}\) and it occurs at \(x = 1\). So, the absolute extrema are \(\boxed{1}\) and \(\boxed{0}\).