Find the relative extrema of the function, if they exist.
\[
f(x)=x^{3}-12 x-2
\]
A. Relative maximum at $(5,63)$; relative minimum at $(-3,7)$
B. Relative maximum at $(5,63)$; relative minimum at $(2,-18)$
C. Relative maximum at $(-2,14)$; relative minimum at $(2,-18)$
D. Relative minimum at $(-2,14)$; relative maximum at $(2,-18)$

Step 1 ：First, we need to find the derivative of the function \(f(x) = x^{3} - 12x - 2\).

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

Step 3 ：Next, we set the derivative equal to zero and solve for x to find the critical points. The critical points are where the function may have relative extrema.

Step 4 ：The critical points are \(x = -2\) and \(x = 2\).

Step 5 ：We then use the second derivative test to determine whether each critical point is a relative maximum, relative minimum, or neither.

Step 6 ：The second derivative of the function is \(f''(x) = 6x\).

Step 7 ：By substituting the critical points into the second derivative, we find that the function has a relative maximum at \((-2,14)\) and a relative minimum at \((2,-18)\).

Step 8 ：\(\boxed{\text{Final Answer: The relative maximum is at }(-2,14)\text{ and the relative minimum is at }(2,-18)}\)