(1) \( f(x)=x^{3}-3 x^{2}-9 x+3 \)

Did you know that the function \( f(x) = x^3 - 3x^2 - 9x + 3 \) can be analyzed for its critical points by finding the derivative and setting it to zero? This polynomial is cubic, which means it can have up to three real roots. Finding these roots can reveal important information about the behavior of the function, including local maxima or minima! To effectively tackle this polynomial, a common approach is to use techniques like synthetic division or the Rational Root Theorem to factor it. After factoring, you can apply the quadratic formula for any remaining quadratic equations. Always double-check your work to avoid common mistakes like overlooking potential complex roots!