2019 Nov P1 Q9

Question 9

Given: $f(x)=3x^3$
$9.1$	Solve $f(x)=f^\prime (x)$	$(3)$
$9.2$	The graphs $f$ , $f^\prime$ and $f^{\prime \prime}$ all pass through the point $(0\; ; \,0)$ .
$\quad 9.2.1$	For which of the graphs will $(0\; ; \,0)$ be a stationary point?	$(1)$
$\quad 9.2.2$	Explain the difference, if any, in the stationary points referred to in QUESTION $9.2.1$ .	$(2)$
$9.3$	Determine the vertical distance between the graphs of $f^\prime$ and $f^{\prime \prime}$ at $x=1$ .	$(3)$
$9.4$	For which value(s) of $x$ is $f(x)-f^\prime (x)<0$ ?	$(4)$
		$\textbf{[13]}$