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:

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

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