Consider the function $f$:$RR$ given by

$f(x)=x^4-50x^2$

$$Find the three critical numbers $a,b,c$ of $f$ and list their exact values in the first column of the table below$$in ascending order $Rf+-fx-a=b=c=x>cb,$Click for List,$a,$Click for List,$x,,a$ The second column consists $of$ several drop$down$ menus$Do$ the following$$

$for$ each $of$ the intervals $ofR$ defined $by$ these points$select$ the phrase that best describes the behaviour $of$ the function $fon$ that interval$$

$for$ each $of$ the critical numbers$select$ the phrase that best describes their nature$$

$for$ each $of+-select$ the phrase that best describes the corresponding $limiting$ behaviour $off$

$\begin{array}{cc}x& \text{B}\text{e}\text{h}\text{a}\text{v}\text{i}\text{o}\text{r}\\ ?& -\\ \text{C}\text{l}\text{i}\text{c}\text{k}\text{f}\text{o}\text{r}\text{L}\text{i}\text{s}\text{t}& \\ x& ?\\ ?& a\\ \text{C}\text{l}\text{i}\text{c}\text{k}\text{f}\text{o}\text{r}\text{L}\text{i}\text{s}\text{t}& \\ a& \text{C}\text{l}\text{i}\text{c}\text{k}\text{f}\text{o}\text{r}\text{L}\text{i}\text{s}\text{t}\\ & b\\ \text{C}\text{l}\text{i}\text{c}\text{k}\text{f}\text{o}\text{r}\text{L}\text{i}\text{s}\text{t}& \\ b& \text{C}\text{l}\text{i}\text{c}\text{k}\text{f}\text{o}\text{r}\text{L}\text{i}\text{s}\text{t}\\ & c\\ \text{C}\text{l}\text{i}\text{c}\text{k}\text{f}\text{o}\text{r}\text{L}\text{i}\text{s}\text{t}& \\ x>c& \text{C}\text{l}\text{i}\text{c}\text{k}\text{f}\text{o}\text{r}\text{L}\text{i}\text{s}\text{t}\\ & \\ \text{C}\text{l}\text{i}\text{c}\text{k}\text{f}\text{o}\text{r}\text{L}\text{i}\text{s}\text{t}& \end{array}>c=>c==>c===$