260109-test

260109-test/20260109_163430_quadratic_vertex工具GithubCopilot模型gemini-3-pro-preview/solve.py

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+# /// script
+# requires-python = ">=3.11"
+# dependencies = ["sympy"]
+# ///
+
+import sympy as sp
+
+def solve():
+    x = sp.symbols('x', real=True)
+    y = -2*x**2 + 8*x - 3
+    
+    # Find derivative to find critical points
+    dy_dx = sp.diff(y, x)
+    critical_points = sp.solve(dy_dx, x)
+    
+    print(f"Critical points (x): {critical_points}")
+    
+    if not critical_points:
+        print("No critical points found.")
+        return
+
+    vertex_x = critical_points[0]
+    vertex_y = y.subs(x, vertex_x)
+    
+    print(f"Vertex: ({vertex_x}, {vertex_y})")
+    
+    # Check second derivative to confirm maximum
+    d2y_dx2 = sp.diff(dy_dx, x)
+    print(f"Second derivative: {d2y_dx2}")
+    
+    if d2y_dx2 < 0:
+        print("The vertex is a maximum.")
+        max_val = vertex_y
+    else:
+        print("The vertex is a minimum.")
+        max_val = vertex_y 
+
+    print(f"Maximum value: {max_val}")
+
+if __name__ == "__main__":
+    solve()