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由于含参不等式恒成立问题将函数、不等式、几何、三角等知识有机地结合在一起,知识点多、覆盖面广、综合性强、解法灵活,在高考及各类数学竞赛中都受命题者喜爱。对这类问题求解时涉及分类讨论、函数与方程、数形结合、化归及转化等数学思想,有效地锻炼了学生的解题能力和思维变换,培养了学生的创新能力。
Due to the inequality of parameter inequality, the knowledge, function, inequality, geometry and trigonometry are organically combined together. The knowledge, the coverage, the comprehensiveness and the flexibility of solution are all favored by the proponents in the college entrance examination and various math competitions . Solving this kind of problem involves mathematical discussions such as category discussion, function and equation, combination of numbers and forms, transformation and conversion, effectively training students’ problem-solving abilities and thinking transformations, and cultivating their innovative abilities.