Question

11£®ÒÑÖªº¯Êýf£¨x£©=xe^x£¬¼Çf₀£¨x£©=f¡ä£¨x£©£¬f₁£¨x£©=f¡ä£¨x₀£©£¬¡­£¬f_n£¨x£©=f¡ä_n-1£¨x£©ÇÒx₂£¾x₁£¬¶ÔÓÚÏÂÁÐÃüÌ⣺
¢Ùº¯Êýf£¨x£©´æÔÚƽÐÐÓÚxÖáµÄÇÐÏߣ»
¢Ú$\frac{f£¨{x}_{1}£©-f£¨{x}_{2}£©}{{x}_{1}-{x}_{2}}$£¾0£»
¢Ûf¡ä₂₀₁₂£¨x£©=xe^x+2014e^x£»
¢Üf£¨x₁£©+x₂£¼f£¨x₂£©+x₁£®
¢Ýµ±x₁£¾0ʱ£¬ÓÐx₂f£¨x₁£©£¼x₁f£¨x₂£©£®
ÆäÖÐÕýÈ·µÄÃüÌâÐòºÅÊǢ٢ۢݣ¨Ð´³öËùÓÐÂú×ãÌâÄ¿Ìõ¼þµÄÐòºÅ£©£®

Answer 1

·ÖÎö ¸ù¾Ýµ¼ÊýµÄ¼¸ºÎÒâÒåÅжϢÙÕýÈ·£¬¸ù¾Ýµ¼ÊýºÍº¯ÊýµÄµ¥µ÷ÐÔÅÐ¶Ï¢Ú´í£»¸ù¾Ýµ¼ÊýµÄÔËË㣬µÃµ½¢ÛÕýÈ·£¬¸ù¾Ýµ¼ÊýÓ뺯ÊýµÄµ¥µ÷ÐԵĹØϵÅÐ¶Ï¢Ü´í£®¸ù¾Ýº¯ÊýµÄбÂʹØϵ£¬½áºÏº¯ÊýµÄµ¥µ÷ÐÔ¿ÉÒÔÅжϢÝÕýÈ·£®

½â´ð ½â£º¢Ù£¬¡ßf¡ä£¨x£©=£¨x+1£©e^x£¬¡àµ±x=-1ʱ£¬f¡ä£¨-1£©=0£¬º¯Êýf£¨x£©´æÔÚƽÐÐÓÚxÖáµÄÇÐÏߣ¬¹Ê¢ÙÕýÈ·£»
¢Ú£¬¡ßf¡ä£¨x£©=£¨x+1£©e^x£¬¡àx¡Ê£¨-¡Þ£¬-1£©Ê±£¬º¯Êýf£¨x£©µ¥µ÷µÝ¼õ£¬x¡Ê£¨-1£¬+¡Þ£©Ê±£¬º¯Êýf£¨x£©µ¥µ÷µÝÔö£¬
¹Ê$\frac{f£¨{x}_{1}£©-f£¨{x}_{2}£©}{{x}_{1}-{x}_{2}}$£¾0²»ÄÜÈ·¶¨£¬¹Ê¢Ú´í£»
¢Û£¬¡ßf₁£¨x£©=f¡ä£¨x₀£©=xe^x+2e^x£¬f₂£¨x£©=f₁¡ä£¨x£©=xe^x+3e^x£¬¡­£¬f_n£¨x£©=f¡ä_n-1£¨x£©=xe^x+£¨n+1£©e^x£¬
¡àf¡ä₂₀₁₂£¨x£©=f₂₀₁₃£¨x£©=xe^x+2014e^x£»¹Ê¢ÛÕýÈ·£»
¢Ü£¬f£¨x₁£©+x₂£¼f£¨x₂£©+x₁µÈ¼ÛÓÚf£¨x₁£©-x₁£¼f£¨x₂£©-x₂£¬¹¹½¨º¯Êýh£¨x£©=f£¨x£©-x£¬Ôòh¡ä£¨x£©=f¡ä£¨x£©-1=£¨x+1£©e^x-1£¬
Ò×Öªº¯Êýh£¨x£©ÔÚRÉϲ»µ¥µ÷£¬¹Ê¢Ü´í£»
¢Ý£¬µ±x₁£¾0ʱ£¬ÓÐx₂f£¨x₁£©£¼x₁f£¨x₂£©£®ÔòµÈ¼ÛΪ$\frac{f£¨{x}_{1}£©}{{x}_{1}}$£¼$\frac{f£¨{x}_{2}£©}{{x}_{2}}$£¬
¼´º¯ÊýÔÚµãA£¨x₁£¬f£¨x₁£©£©£¬B£¨x₂£¬f£¨x₂£©£©´¦£¬ÓëÔ­µãµÄбÂÊÂú×ãk_OA£¼k_OB£¬
ÓÉ¢ÚÖªº¯ÊýÔÚ£¨0£¬+¡Þ£©Éϵ¥µ÷µÝÔö£¬Ôòk_OA£¼k_OB£¬³ÉÁ¢£¬¹Ê¢ÝÕýÈ·£¬
¹Ê´ð°¸Îª£º¢Ù¢Û¢Ý

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éÓëµ¼ÊýÓйصÄÃüÌâµÄÕæ¼ÙÅжϣ¬¿¼²éÁ˵¼ÊýµÄ¼¸ºÎÒâÒåÒÔ¼°µ¼ÊýºÍº¯ÊýµÄµ¥µ÷ÐԵĹØϵ£¬ÒÔ¼°µ¼ÊýµÄÔËËã·¨Ôò£¬ÊôÓÚÖеµÌâ