What are the minimum and maximum values of x, for which x3 + x2 – 6x ≥ 0?

Factor the expression: x³ + x² − 6x = x(x + 3)(x − 2). Its zeros are −3, 0, and 2; checking the signs between them shows the expression is nonnegative on [−3, 0] and [2, ∞). The smallest solution is −3, and the solutions continue upward without bound, so there is no maximum. The correct choice is “minimum = −3, no maximum.”

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