Use the graph of the given function to find any relative maxima and relative minima. \[ f(x)=x^{3}-3 x^{2}+1 \]

Step 1 ：Given the function \(f(x)=x^{3}-3 x^{2}+1\), we want to find any relative maxima and minima.

Step 2 ：We start by taking the derivative of the function, \(f'(x) = 3x^{2} - 6x\).

Step 3 ：We set the derivative equal to zero and solve for x to find the critical points, which gives us \(x = 0\) and \(x = 2\).

Step 4 ：We then take the second derivative of the function, \(f''(x) = 6x - 6\).

Step 5 ：We substitute the critical points into the second derivative. If the second derivative at a critical point is positive, the point is a relative minimum. If it's negative, the point is a relative maximum. If it's zero, the test is inconclusive.

Step 6 ：Substituting \(x = 0\) into the second derivative gives a negative value, so \(x = 0\) is a relative maximum.

Step 7 ：Substituting \(x = 2\) into the second derivative gives a positive value, so \(x = 2\) is a relative minimum.

Step 8 ：\(\boxed{\text{Final Answer: The relative maximum of the function } f(x)=x^{3}-3 x^{2}+1 \text{ is at } x=0 \text{ and the relative minimum is at } x=2}\)