What are the minimum and maximum values of x, for which x3 + x2 – 6x ≥ 0? minimum = –3, maximum = 0 minimum = 0, maximum = 2 minimum = –3, no maximum minimum = 2, no maximum Please answer quickly

Option C.

Step-by-step explanation:

The given inequality is

Taking x common, we get

Splitting the middle term, we get

Related equation is

These three points divide the number line in 4 parts.

Interval       Sign of      Statement

(-∞,-3)                                         False      

(-3,0)                                          True  

(0,2)                                            False      

(2,∞)                                            True  

So, the solution set is (-3,0) ∪ (2,∞).

Thus, minimum value is –3 and no maximum value.

Therefore, the correct option is C.

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