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

Question

1721 views around the world

You can reuse this answer
Creative Commons License

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 $x in [2, +oo[$

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