How do you solve $x (4 - x) (x - 6) \leq 0$ $x(4-x)(x-6)<=0$ ?

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How do you solve $x (4 - x) (x - 6) \leq 0$ $x(4-x)(x-6)<=0$ ?

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Answer 1 · 2016-11-19T07:01:16

The answer is $x \in [0, 4] \cup [6, + \infty [$ $x in [0,4] uu [6,+ oo[$

Explanation:

Let $f (x) = x (4 - x) (x - 6)$ $f(x)=x(4-x)(x-6)$

Let's do a sign chart

$a a a a$ $color(white)(aaaa)$ $x$ $x$ $a a a a$ $color(white)(aaaa)$ $- \infty$ $-oo$ $a a a a$ $color(white)(aaaa)$ $0$ $0$ $a a a a a$ $color(white)(aaaaa)$ $4$ $4$ $a a a a a a$ $color(white)(aaaaaa)$ $6$ $6$ $a a a a a a$ $color(white)(aaaaaa)$ $+ \infty$ $+oo$

$a a a a$ $color(white)(aaaa)$ $x$ $x$ $a a a a a a a$ $color(white)(aaaaaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $+$ $+$ $a a a a$ $color(white)(aaaa)$ $+$ $+$ $a a a a$ $color(white)(aaaa)$ $+$ $+$

$a a a a$ $color(white)(aaaa)$ $4 - x$ $4-x$ $a a a a$ $color(white)(aaaa)$ $+$ $+$ $a a a a$ $color(white)(aaaa)$ $+$ $+$ $a a a a$ $color(white)(aaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $-$ $-$

$a a a a$ $color(white)(aaaa)$ $x - 6$ $x-6$ $a a a a$ $color(white)(aaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $+$ $+$

$a a a a$ $color(white)(aaaa)$ $f (x)$ $f(x)$ $a a a a a$ $color(white)(aaaaa)$ $+$ $+$ $a a a a$ $color(white)(aaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $+$ $+$ $a a a a$ $color(white)(aaaa)$ $-$ $-$

For $f (x) \leq 0$ $f(x)<=0$

The solution is $x \in [0, 4] \cup [6, + \infty [$ $x in [0,4] uu [6,+ oo[$
graph{x(4-x)(x-6) [-14.56, 13.9, -8.47, 5.77]}

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How do you solve $x (4 - x) (x - 6) \leq 0$ $x(4-x)(x-6)<=0$ ?

1 Answer

Explanation:

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How do you solve x(4-x)(x-6)<=0x(4−x)(x−6)≤0x(4-x)(x-6)<=0?

1 Answer

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How do you solve $x (4 - x) (x - 6) \leq 0$ $x(4-x)(x-6)<=0$ ?