Let $p(z) = 2z^4 - 4z^2 + 6$.
Fill in the values or intervals below.
If there is nothing applicable for a given category enter NONE. For $\infty$ use infinity. For $-\infty$, use -infinity. To indicate a union of intervals, use U.
interval(s) on which $p$ is increasing $(-1,0) \cup (1,\infty)$
interval(s) on which $p$ is decreasing $(-\infty,-1) \cup (0,1)$
point(s) at which $p$ achieves a local maximum $(0,6)$
point(s) at which $p$ achieves a local minimum $(-1,4),(1,4)$
interval(s) on which $p$ is concave up $(-\infty, -\frac{\sqrt{3}}{3}) \cup (-\frac{\sqrt{3}}{3}, \infty)$
interval(s) on which $p$ is concave down $(-\frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3})$
Use your results, as recorded above, to sketch the graph of $p$. Check by making a plot. (not submitted).
