增函数减减函数后是什么函数?反之呢？ 增函数加或减一个减函数后是什么函数?为什么?
\u600e\u4e48\u8bc1\u660e\u51fd\u6570\u662f\u589e\u51fd\u6570\u8fd8\u662f\u51cf\u51fd\u6570\uff1f\u5148\u8bbe\u5728\u51fd\u6570\u5b9a\u4e49\u57df\u4e0a\uff0c\u6216\u5728\u5b9a\u4e49\u57df\u7684\u67d0\u6bb5\u533a\u95f4\u4e0ax1<x2\uff0c
\u7136\u540e\u6839\u636ef(x2)-f(x1)\u4e0e0\u7684\u5927\u5c0f\u5173\u7cfb\uff0c\u6765\u5224\u65ad\u51fd\u6570\u7684\u589e\u51cf\u6027\u3002
\u5982\uff1a\u8bc1\u660e\u51fd\u6570f\uff08x\uff09=x²+a\u5728\uff080\uff0c+\u221e\uff09\u4e0a\u7684\u5355\u8c03\u6027
\u8bc1\u660e\uff1a\u8bbe0<x1<x2<+\u221e\uff0c
f(x2)-f(x1)=\uff08x²2+a\uff09-\uff08x²1+a\uff09
=x²2-x²1>0
\u5373f(x2)>f(x1)
\u6240\u4ee5\u51fd\u6570f\uff08x\uff09=x²+a\u5728\uff080\uff0c+\u221e\uff09\u4e0a\u7684\u5355\u8c03\u589e\u51fd\u6570\u3002
\u52a0\u4e00\u4e2a\u51cf\u51fd\u6570\u540e\u6709\u53ef\u80fd\u589e,\u4e5f\u53ef\u80fd\u51cf,\u4e5f\u53ef\u80fd\u975e\u5355\u8c03,\u8981\u770b\u8c01\u7684\u589e\u51cf\u901f\u5ea6\u5feb.
\u51cf\u4e00\u4e2a\u51cf\u51fd\u6570\u540e\u5219\u4e00\u5b9a\u662f\u589e\u51fd\u6570.\u76f8\u5f53\u4e8e\u4e24\u4e2a\u589e\u51fd\u6570\u76f8\u52a0.
绛旓細澧炲嚱鏁-鍑忓嚱鏁颁负澧炲嚱鏁锛屽洜涓哄鍑芥暟-鍑忓嚱鏁颁篃灏辨槸澧炲嚱鏁+澧炲嚱鏁帮紝鏍规嵁鍚屽寮傚噺鍘熺悊寰楀嚭浠嶄负澧炲嚱鏁帮紝鑰屽鍑芥暟+鍑忓嚱鏁板垯涓嶈兘鍒ゆ柇鍏朵负浠涔堝嚱鏁帮紝鍏抽敭鐪嬪鍑芥暟澧為暱鐨勯熷害鍜屽噺鍑芥暟鍑忓皯鐨勭▼搴﹀ぇ灏忥紝鐒跺悗鍐嶅垽鏂
绛旓細2銆佸噺鍑芥暟+鍑忓嚱鏁=鍑忓嚱鏁 3銆佸鍑芥暟-鍑忓嚱鏁=澧炲嚱鏁 4銆佸噺鍑芥暟-澧炲嚱鏁=鍑忓嚱鏁 5銆佸鍑芥暟-澧炲嚱鏁=涓嶈兘纭畾 6銆佸噺鍑芥暟-鍑忓嚱鏁=涓嶈兘纭畾 璁惧嚱鏁癴(x)鐨勫畾涔夊煙涓篋锛屽鏋滃浜庡畾涔夊煙D鍐呯殑鏌愪釜鍖洪棿涓婄殑浠绘剰涓や釜鑷彉閲忕殑鍊紉1, x2锛屽綋x1<x2鏃堕兘鏈塮(x1)<f(x2)锛岄偅涔堝氨璇磃(x)鍦ㄦ鍖洪棿涓婃槸澧...
绛旓細澧炲嚱鏁-鍑忓嚱鏁=澧炲嚱鏁 鍑忓嚱鏁-澧炲嚱鏁=鍑忓嚱鏁 澧炲嚱鏁-澧炲嚱鏁=涓嶈兘纭畾 鍑忓嚱鏁-鍑忓嚱鏁=涓嶈兘纭畾
绛旓細澧炲嚱鏁-鍑忓嚱鏁=澧炲嚱鏁銆傝鍑芥暟f锛坸锛夌殑瀹氫箟鍩熶负D锛屽鏋滃浜庡畾涔夊煙D鍐呯殑鏌愪釜鍖洪棿涓婄殑浠绘剰涓や釜鑷彉閲忕殑鍊紉1锛寈2锛屽綋x1f锛坸2锛夛紝閭ｄ箞灏辫f锛坸锛夊湪杩欎釜鍖洪棿涓婃槸鍑忓嚱鏁帮紝骞剁О鍖洪棿D涓洪掑噺鍖洪棿銆傚噺鍑芥暟鐨勫浘鍍忎粠宸﹀線鍙虫槸涓嬮檷鐨勶紝鍗冲嚱鏁板奸殢鑷彉閲忕殑澧炲ぇ鑰屽噺灏忋傚垽鏂竴涓嚱鏁版槸鍚︿负鍑忓嚱鏁板彲浠ラ氳繃瀹氫箟娉...
绛旓細澧炲嚱鏁般傛牴鎹煡璇綔涓氬府瀹樼綉寰楃煡锛澧炲嚱鏁板噺鍑忓嚱鏁绛夊鍑芥暟锛屽鍑芥暟涔樺噺鍑芥暟绛変簬鍑忓嚱鏁帮紝澧炲嚱鏁伴櫎鍑忓嚱鏁扮瓑浜庡鍑芥暟銆傚鍑芥暟鏈変袱涓噸瑕佺殑鎬ц川锛屽叾涓鏄崟璋冩э紝鍗冲鍑芥暟鐨勫嚱鏁板煎彧鏈夊鍔犵殑鍙兘锛岃屼笉鑳藉噺灏戯紱鍏朵簩鏄繛缁э紝鍗冲鍑芥暟鐨勫嚱鏁板奸殢鐫鑷彉閲忕殑鍙樺寲杩炵画鍙樺寲锛岃屼笉浼氬嚭鐜版柇宕栫姸鐨勫彉鍖栥
绛旓細澧炲嚱鏁板噺鍘讳竴涓鍑忓嚱鏁鎵寰楃殑鏂板嚱鏁帮紝闅忕潃鑷彉閲忕殑澧炲ぇ锛屽嚱鏁板艰秼浜庡ぇ鍊煎噺灏忓硷紝鏁呬负澧炲嚱鏁般
绛旓細澧炲嚱鏁+澧炲嚱鏁=澧炲嚱鏁帮紝澧炲嚱鏁-鍑忓嚱鏁=澧炲嚱鏁帮紝鍑忓嚱鏁+鍑忓嚱鏁=鍑忓嚱鏁帮紝鍑忓嚱鏁-澧炲嚱鏁=鍑忓嚱鏁般傝屽鍑芥暟+鍑忓嚱鏁扮殑澧炲噺鎬т笉涓瀹氱殑銆備竴鑸湴锛岃鍑芥暟f锛坸锛夌殑瀹氫箟鍩熶负D锛屽鏋滃浜庡畾涔夊煙D鍐呯殑鏌愪釜鍖洪棿涓婄殑銆備换鎰忎袱涓嚜鍙橀噺鐨勫紉1锛寈2锛屽綋x1<x2鏃讹紝閮芥湁f锛坸1锛<f锛坸2锛夛紝閭ｄ箞灏辫f锛坸锛夊湪...
绛旓細鍙兘纭畾鐨勬槸 澧炲嚱鏁鍜屽噺鍑芥暟浜岃呯浉鍑 寰楀埌鐨勫氨鏄鍑芥暟 鍚岀悊鍑忓嚱鏁板噺鍘诲鍑芥暟寰楀埌鍑忓皯 瀵逛簬鐩镐箻鐩搁櫎鐨勮瘽 閮藉彲鑳戒細瀛樺湪姝ｈ礋鍙风殑鍙樺寲闂 涓嶈兘瀹屽叏纭畾
绛旓細鍒欏嚱鏁癰锛媋f锛坸锛夊湪I涓婇掑噺锛庡嵆鍒ゆ柇F锛圶1锛-F(X2)锛堝叾涓璛1鍜孹2灞炰簬瀹氫箟鍩燂紝鍋囪X1<X2).鑻ヨ寮忓ぇ浜庨浂锛屽垯鍦ㄥ畾涔夊煙鍐匜(X)涓鍑忓嚱鏁锛涚浉鍙嶏紝鑻ヨ寮忓皬浜庨浂锛屽垯鍦ㄥ畾涔夊煙鍐呭嚱鏁颁负澧炲嚱鏁銆傦紙瑕佹敞鎰忕殑鏄湪瀹氫箟鍩熷唴锛屽嚱鏁版棦鍙兘涓哄鍑芥暟锛屼篃鍙兘涓哄噺鍑芥暟锛屽叿浣撴儏鍐佃鐪嬫眰鍑烘潵鐨剎鐨勮寖鍥淬
绛旓細鍔犱竴涓鍑忓嚱鏁板悗鏈夊彲鑳藉,涔熷彲鑳藉噺,涔熷彲鑳介潪鍗曡皟,瑕佺湅璋佺殑澧炲噺閫熷害蹇.鍑忎竴涓噺鍑芥暟鍚庡垯涓瀹氭槸澧炲嚱鏁.鐩稿綋浜庝袱涓鍑芥暟鐩稿姞.
