Science:Math Exam Resources/Courses/MATH102/December 2011/Question 04 (iv)/Solution 1

In part ii) of this question we obtained the sign table of the derivative:

		$0$		$3$
$x$	$-$	$0$	$+$		$+$
$(x-3{)}^2$	$+$		$+$	$0$	$+$
$f^{\prime }(x)$	$-$	$0$	$+$	$0$	$+$
$f(x)$	$\searrow$		$\nearrow$		$\nearrow$

And we see there that the function is decreasing on the interval (-∞,0) and increasing on the intervals (0,3) and (3,+∞).