260109-test

260109-test/20260109_quadratic_vertex_max-工具opencode模型GLM47/solve.py

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+# /// script
+# requires-python = ">=3.11"
+# dependencies = ["sympy"]
+# ///
+
+import sympy as sp
+
+# 定义符号（实数）
+x = sp.symbols("x", real=True)
+
+# 定义函数
+y = -2 * x**2 + 8 * x - 3
+
+# 方法1：通过顶点公式求解
+# 二次函数 y = ax^2 + bx + c 的顶点公式：x = -b/(2a)
+a = -2
+b = 8
+c = -3
+
+x_vertex = -b / (2 * a)
+y_vertex = a * x_vertex**2 + b * x_vertex + c
+
+# 方法2：通过求导验证
+dy_dx = sp.diff(y, x)
+critical_points = sp.solve(dy_dx, x)
+d2y_dx2 = sp.diff(dy_dx, x)
+
+print("=" * 50)
+print("二次函数：y = -2x² + 8x - 3")
+print("=" * 50)
+
+print("\n【方法1：顶点公式】")
+print(f"顶点坐标：({x_vertex}, {y_vertex})")
+
+print("\n【方法2：求导法】")
+print(f"导数：y' = {dy_dx}")
+print(f"二阶导数：y'' = {d2y_dx2}")
+print(f"临界点：x = {critical_points[0]}")
+print(f"代入原函数：y = {y.subs(x, critical_points[0])}")
+print(f"二阶导数：{d2y_dx2} < 0，故为极大值点")
+
+print("\n【结论】")
+print(f"1. 顶点坐标：({x_vertex}, {y_vertex})")
+print(f"2. 函数最大值：{y_vertex}")