Question 912702
{{{x^4>x^2}}}
{{{x^4-x^2>0}}}
{{{x^2(x^2-1)>0}}}
{{{x^2(x-1)(x+1)>0}}}
Three critical points : {{{x=0}}},{{{x=1}}},{{{x=-1}}}
Break up the number line into 4 regions,
Region 1 : {{{x<-1}}}
Region 2 : {{{-1<x<0}}}
Region 3 : {{{0<x<1}}}
Region 4 : {{{x>1}}}
Pick a point in each region (not the endpoint) and test the inequality.
If the inequality is satisfied the region is part of the solution.
Region 1 : {{{x=-2}}}
{{{4(-3)(-1)>0}}}
{{{12>0}}}
True, part of the solution region.
Region 2 : {{{x=-1/2}}}
{{{(1/4)(-3/2)(1/2)>0}}}
{{{-3/16>0}}}
False.
Region 3 : {{{x=1/2}}}
{{{(1/4)(-1/2)(3/2)>0}}}
{{{-3/16>0}}}
False.
Region 4: {{{x=2}}}
{{{4(1)(3)>0}}}
{{{12>0}}}
True, part of the solution region.
Now put it all together,
({{{-infinity}}},{{{-1}}})U({{{1}}},{{{infinity}}})
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{{{graph(300,300,-3,3,-1,3,x^4,x^2)}}}
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{{{x^4}}} in Red
{{{x^2}}} in Green