(2) Given the cubic function $f(x)=a x^{3}+b x^{2}+c x+d,(a, b, c, d \in \mathbf{R})$, proposition $p: y=f(x)$ is a monotonic function on $\mathbf{R}$;
proposition $q: y=f(x)$ intersects the $x$-axis at exactly one point. Then $p$ is ( ) of $q$.
(A) a sufficient but not necessary condition
(B) a necessary but not sufficient condition
(C) a necessary and sufficient condition
(D) neither a sufficient nor a necessary condition
(2) A