导数取点

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@user_c458f2f4/derivative-point-picking

导数取点.skill 是一个面向高考导数压轴题的 AI Skill，专注于零点存在性、零点个数与参数范围证明。它引导 AI 先用导数、单调性、极值与极限分析题目，再把“显然存在”“趋于无穷”这类不够稳妥的表述，改写成具体取点、函数值异号、连续性与零点存在定理的阅卷友好证明。同时，它会解释取点来源，帮助学生理解为什么取这个点，而不是只看到一个突然出现的“神奇点”。 Solve high-school or college-entrance-exam style derivative problems centered on root existence, root count, and parameter ranges. Use when a problem asks whether a function has roots/intersections, exactly how many roots it has, or which parameters make roots exist. The skill analyzes with derivatives, monotonic intervals, extrema, limits, and value ranges, then rewrites the final proof using concrete point selection, sign changes, continuity, and the intermediate value theorem. In teaching mode, explain where chosen points come from using tangent bounds, exponential/log inequalities, Taylor-style estimates, quadratic fitting, homomorphic transformations, or explicit threshold solving.