18. \( f(x)=x^{3}+9 x^{2}+6 \)

Did you know that the function \( f(x) = x^{3} + 9x^{2} + 6 \) represents a cubic polynomial? Cubic polynomials can have fascinating shapes, including inflection points where they change concavity, as well as up to three real roots where they intersect the x-axis. Their behavior is influenced heavily by the leading coefficient and the nature of the roots. If you're diving into this polynomial, a great technique is to use the Rational Root Theorem to check possible rational roots systematically. But beware of common mistakes, like overlooking the end behavior of cubic functions! As \( x \) approaches infinity or negative infinity, the \( x^{3} \) term dominates, leading to the function tending towards positive or negative infinity respectively.