Answer: Option C.
Step-by-step explanation:
The given inequality is
[tex]x^3+x^2-6x\geq 0[/tex]
Taking x common, we get
[tex]x(x^2+x-6)\geq 0[/tex]
Splitting the middle term, we get
[tex]x(x^2+3x-2x-6)\geq 0[/tex]
[tex]x(x(x+3)-2(x+3))\geq 0[/tex]
[tex]x(x+3)(x-2)\geq 0[/tex]
Related equation is
[tex]x(x+3)(x-2)=0[/tex]
[tex]x=-3,0,2[/tex]
These three points divide the number line in 4 parts.
Interval Sign of [tex]x(x+3)(x-2)\geq 0[/tex] Statement
(-∞,-3) [tex](-)(-)(-)=(-)[/tex] False
(-3,0) [tex](-)(+)(-)=(+)[/tex] True
(0,2) [tex](+)(+)(-)=(-)[/tex] False
(2,∞) [tex](+)(+)(+)=(+)[/tex] True
So, the solution set is (-3,0) ∪ (2,∞).
Thus, minimum value is –3 and no maximum value.
Therefore, the correct option is C.
Answer:
minimum = –3, no maximum
Step-by-step explanation:
The other guy here was completely correct, but just in case it assures anyone's doubts:
