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

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

		$\displaystyle 1$		$\displaystyle 3$
$\displaystyle 3(x-1)$	$\displaystyle -$	$\displaystyle 0$	$\displaystyle +$		$\displaystyle +$
$\displaystyle (x-3)$	$\displaystyle -$		$\displaystyle -$	$\displaystyle 0$	$\displaystyle +$
$\displaystyle f'(x)$	$\displaystyle +$	$\displaystyle 0$	$\displaystyle -$	$\displaystyle 0$	$\displaystyle +$
$\displaystyle f(x)$	$\displaystyle \cup$		$\displaystyle \cap$		$\displaystyle \cup$

And so we see that function is concave up on the intervals (-∞, 1) and (3, +∞) while it is concave down on the interval (1,3).