<PRE><B>Question 999407</B>
It is possible to have the increasing/decreasing intervals not alternate. There is no rule that says they have to alternate. You can easily have &quot;decreasing, increasing, increasing&quot; which is the case here



Answer: 


Increasing Interval: &lt;img src=&quot;http://www.sciweavers.org/tex2img.php?eq=%5Cleft%28-%5Cfrac%7B3%7D%7B2%7D%2C%200%5Cright%29%20%5Ccup%20%280%2C%5Cinfty%29&amp;bc=White&amp;fc=Black&amp;im=jpg&amp;fs=12&amp;ff=arev&amp;edit=0&quot; align=&quot;center&quot; border=&quot;0&quot; alt=&quot;\left(-\frac{3}{2}, 0\right) \cup (0,\infty)&quot; width=&quot;144&quot; height=&quot;47&quot; /&gt;


Decreasing Interval: &lt;img src=&quot;http://www.sciweavers.org/tex2img.php?eq=%5Cleft%28-%5Cinfty%2C%20-%5Cfrac%7B3%7D%7B2%7D%5Cright%29&amp;bc=White&amp;fc=Black&amp;im=jpg&amp;fs=12&amp;ff=arev&amp;edit=0&quot; align=&quot;center&quot; border=&quot;0&quot; alt=&quot;\left(-\infty, -\frac{3}{2}\right)&quot; width=&quot;94&quot; height=&quot;47&quot; /&gt;



Side Note: the local min occurs at x = -3/2. There is NO local min at x = 0 because we do NOT have a sign change in f &#39; (x) when we pass through x = 0.</PRE>