Find the $x$-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. \[ f(x)=x^{3}-3 x^{2}-9 x+6 \] Select the correct choice below and, if necessary, fill in the answer boxes within your choice. A. There are no relative minima. The function has a relative maximum of $\square$ at $x=\square$. (Type exact answers. Use a comma to separate answers as needed.) B. There are no relative maxima. The function has a relative minimum of $\square$ at $x=\square$. (Type exact answers. Use a comma to separate answers as needed.) C. The function has a relative maximum of $\square$ at $x=\square$ and a relative minimum of $\square$ at $x=\square$. (Type exact answers. Use a comma to separate answers as needed.) D. There are no relative extrema.

Step 1 ：Find the derivative of the function: \(f'(x) = 3x^2 - 6x - 9\)

Step 2 ：Set the derivative equal to zero: \(3x^2 - 6x - 9 = 0\)

Step 3 ：Simplify the equation: \(x^2 - 2x - 3 = 0\)

Step 4 ：Factor the equation: \((x - 3)(x + 1) = 0\)

Step 5 ：Solve for x to find the critical points: \(x = 3\) and \(x = -1\)

Step 6 ：Find the second derivative of the function: \(f''(x) = 6x - 6\)

Step 7 ：Evaluate the second derivative at \(x = 3\): \(f''(3) = 12\)

Step 8 ：Since the second derivative at \(x = 3\) is positive, \(x = 3\) is a relative minimum

Step 9 ：Evaluate the second derivative at \(x = -1\): \(f''(-1) = -12\)

Step 10 ：Since the second derivative at \(x = -1\) is negative, \(x = -1\) is a relative maximum

Step 11 ：Substitute \(x = 3\) into the original function to find the y-value of the relative minimum: \(f(3) = -9\)

Step 12 ：Substitute \(x = -1\) into the original function to find the y-value of the relative maximum: \(f(-1) = 11\)

Step 13 ：\(\boxed{\text{The function has a relative maximum of 11 at x = -1 and a relative minimum of -9 at x = 3}}\)