How do you solve #x^4(x-2)>=0# using a sign chart?

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Answer 1 · 2016-12-30T06:56:22

The answer is #x in [2, +oo[#

Let #f(x)=x^4(x-2)#

The domain of #f(x)# is #D_f(x)=RR#

#AA x in RR, x^4>=0#

The sign chart is very simple

#color(white)(aaaa)##x##color(white)(aaaaaa)##-oo##color(white)(aaaaaa)##2##color(white)(aaaaaa)##+oo#

#color(white)(aaaa)##x-2##color(white)(aaaaaaa)##-##color(white)(aaaaaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaaaa)##-##color(white)(aaaaaaa)##+#

Therefore,

#f(x)>=0#, when # x in [2, +oo[#