设函数y=f（x）的定义域为I，如果存在实数M满足：①对于任意实数x∈I，都有f(x)≤M，②存在
\u5b9a\u4e49\u51fd\u6570y=f\uff08x\uff09\uff1a\u5bf9\u4e8e\u4efb\u610f\u6574\u6570m\uff0c\u5f53\u5b9e\u6570x\u2208(m?12\uff0cm+12)\u65f6\uff0c\u6709f\uff08x\uff09=m\uff0e\uff08\u2160\uff09\u8bbe\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u4e3aD\uff0c\u753b\uff08I\uff09\u5f53x\u2208[0\uff0c12\uff09\u65f6\uff0cf\uff08x\uff09=0\uff0c\u5f53x\u2208[12\uff0c32\uff09\u65f6\uff0cf\uff08x\uff09=1\uff0c\u5f53x\u2208[32\uff0c52\uff09\u65f6\uff0cf\uff08x\uff09=2\uff0c\u5f53x\u2208[52\uff0c72\uff09\u65f6\uff0cf\uff08x\uff09=3\uff0c\u5f53x\u2208[52\uff0c4]\u65f6\uff0cf\uff08x\uff09=4\uff0c\u2234\u56fe\u8c61\u5982\u56fe\u6240\u793a\uff0c\uff08II\uff09\u7531\u4e8ean\uff1d2+10?(25)n\uff0c\u6240\u4ee5f(an)\uff1d6\uff0cn\uff1d14\uff0cn\uff1d23\uff0cn\uff1d32\uff0cn\u22654\uff0c\u56e0\u6b64Sn\uff1d6\uff0cn\uff1d110\uff0cn\uff1d22n+7\uff0cn\u22653\uff1b\uff08III\uff09\u7531f\uff08b1\uff09+f\uff08b2\uff09+f\uff08b3\uff09=4\uff0c\u4e14b1=1\uff0c\u5f97f\uff08q\uff09+f\uff08q2\uff09=3\uff0c\u5f530\uff1cq\u22641\u65f6\uff0c\u5219q2\u2264q\u22641\uff0c\u6240\u4ee5f\uff08q2\uff09\u2264f\uff08q\uff09\u2264f\uff081\uff09=1\uff0c\u5219f\uff08q\uff09+f\uff08q2\uff09\u22642\uff1c3\uff0c\u4e0d\u5408\u9898\u610f\uff1b\u5f53q\uff1e1\u65f6\uff0c\u5219q2\uff1eq\uff1e1\uff0c\u6240\u4ee5f\uff08q2\uff09\u2265f\uff08q\uff09\u2265f\uff081\uff09=1\uff0e\u53c8f\uff08q\uff09+f\uff08q2\uff09=3\uff0c\u2234\u53ea\u53ef\u80fd\u662f<div style="background-image: url(http://hiphotos.baidu.com/zhidao/pic/item/50da81cb39dbb6fd0ba3af920a24ab18962b378d.jpg); background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; width: 9px; overflow-x: hidden; overflow-y:
y=f\uff08x\uff09\u7684\u6700\u5c0f\u503c\u7684\u5b9a\u4e49\u662f\u8fd9\u6837\u7684\uff1a
\u8bbe\u51fd\u6570y=f\uff08x\uff09\u7684\u5b9a\u4e49\u57df\u4e3aI\uff0c\u5982\u679c\u5b58\u5728\u5b9e\u6570M\u6ee1\u8db3\uff1a\u2460\u5bf9\u4e8e\u4efb\u610f\u5b9e\u6570x\u2208I\uff0c\u90fd\u6709f(x)\u2265M\uff0c\u2461\u5b58\u5728x0\u2208I\u3002\u4f7f\u5f97f (x0)=M\uff0c\u90a3\u4e48\uff0c\u6211\u4eec\u79f0\u5b9e\u6570M \u662f\u51fd\u6570y=f(x)\u7684\u6700\u5c0f\u503c\u3002
\u4e5f\u5c31\u662f\u8bf4,\u5bf9\u4efb\u610fx\u2208I,\u5b58\u5728x0\u2208I,,\u4f7ff(x)\u2265f\uff08x0)=M
你想的太简单了
绛旓細璁惧嚱鏁皔=f锛坸锛夌殑瀹氫箟鍩熶负I锛屽鏋滃瓨鍦ㄥ疄鏁癕婊¤冻锛氣憼瀵逛簬浠绘剰瀹炴暟x鈭圛锛岄兘鏈塮(x)鈮锛屸憽瀛樺湪x0鈭圛銆備娇寰梖(x0)=M锛岄偅涔堬紝鎴戜滑绉板疄鏁癕鏄嚱鏁皔=f(x)鐨勬渶灏忓笺傝鍑芥暟y=f锛坸锛夌殑瀹氫箟鍩熶负I锛屽鏋滃瓨鍦ㄥ疄鏁癕婊¤冻锛氣憼瀵逛簬浠绘剰瀹炴暟x鈭圛锛岄兘鏈塮(x)鈮锛屸憽瀛樺湪x0鈭圛銆備娇寰梖(x0)=M锛岄偅涔...
绛旓細鍦ㄦ暣涓畾涔夊煙鍖洪棿锛y=x閮芥槸鍗曞鍖洪棿锛屼篃灏辨槸鍗曞鍖洪棿涓簒鈭圧 涓鑸湴锛璁惧嚱鏁癴(x)鐨勫畾涔夊煙涓篒锛歽=x鐨勫浘鍍 鍗曡皟鍑芥暟 濡傛灉瀵逛簬灞炰簬I鍐呮煇涓尯闂翠笂鐨勪换鎰忎袱涓嚜鍙橀噺鐨勫紉1銆亁2,褰搙1<x2鏃堕兘鏈塮(x1)< f(x2).閭ｄ箞灏辫f(x)鍦ㄨ繖涓尯闂翠笂鏄鍑芥暟.濡傛灉瀵逛簬灞炰簬I鍐呮煇涓尯闂翠笂鐨勪换鎰忎袱涓嚜鍙橀噺鐨...
绛旓細鍒╃敤鍩烘湰涓嶇瓑寮弝=1/2{2x(4-2x)鈮1/2锛2x+4-2x锛/2}²=2 鍗充粎褰2x=4-2x鏃讹紝鍗硏=1鏃讹紝ymax=2 鎴栧埄鐢ㄤ簩娆″嚱鏁版眰鏈鍊硷紝y=0锛屼袱鏍逛负0,2閭ｄ箞瀵圭О杞磝=1锛屽嵆褰搙=1鏃讹紝yamx=2 鏈灏忓 璁惧嚱鏁皔=f锛坸锛夌殑瀹氫箟鍩熶负I锛屽鏋滃瓨鍦ㄥ疄鏁癕婊¤冻锛氣憼瀵逛簬浠绘剰瀹炴暟x鈭圛锛岄兘鏈塮(x)鈮锛...
绛旓細涓句釜渚嬪瓙锛屽弽姣斾緥鍑芥暟鏄竴涓叿鏈夊崟璋冩х殑鍑芥暟锛岃屼笉鏄竴涓崟璋冨嚱鏁帮紝鍥犱负鍦ㄥ弽姣斾緥鍑芥暟鐨勫畾涔夊煙涓婏紝骞朵笉鍛堢幇鏁翠綋鐨勫崟璋冩с傚崟璋冨嚱鏁板彧鏄崟璋冩у嚱鏁颁腑鐗规畩鐨勪竴绉嶃傚尯闂村叿鏈夊崟璋冩х殑鍑芥暟骞朵笉涓瀹氭槸鍗曡皟鍑芥暟锛岃屽崟璋冨嚱鏁扮殑瀛愬尯闂翠笂涓瀹氬叿鏈夊崟璋冩с傚叿鏈夊崟璋冩у嚱鏁板彲浠ユ牴鎹尯闂翠笉鍚岃屽崟璋冩т笉鍚屻
绛旓細棣栧厛涓涓繀椤绘槑纭殑闂鏄紝鑲畾涓嶈兘鏈夌瓑鍙凤紝x1=x2,杩欐牱鏄病鏈夋剰涔夌殑锛屾樉鐒秄(x1)=f(x2).鍏舵锛屽鍑鍑芥暟瀹氫箟鐨璇濓紝涓昏鏄湅涓や釜涓嶇瓑寮忕鍙风殑鏂瑰悜鐨勶紝鍚屽悜灏卞锛屽弽鍚戝氨鍑忥紝骞朵笉鏄竴瀹氳x1<x2
绛旓細璧勬枡鎵╁睍锛氫竴鑸殑锛屽嚱鏁版渶鍊煎垎涓哄嚱鏁版渶灏忓间笌鍑芥暟鏈澶у笺傜畝鍗曟潵璇达紝鏈灏忓煎嵆瀹氫箟鍩熶腑鍑芥暟鍊肩殑鏈灏忓硷紝鏈澶у煎嵆瀹氫箟鍩熶腑鍑芥暟鍊肩殑鏈澶у笺傚嚱鏁版渶澶э紙灏)鍊肩殑鍑犱綍鎰忎箟鈥斺斿嚱鏁板浘鍍忕殑鏈楂橈紙浣庯級鐐圭殑绾靛潗鏍囧嵆涓鸿鍑芥暟鐨勬渶澶э紙灏忥級鍊笺1銆佹渶灏忓 璁惧嚱鏁皔=f(x)鐨勫畾涔夊煙涓篒锛屽鏋滃瓨鍦ㄥ疄鏁癕婊¤冻...
绛旓細浜屻佸叧浜庡绉拌酱鐨勬眰娉曘1銆佸亣璁鍑芥暟y=f(x)鐨勫畾涔夊煙涓篒锛屽鏋滃浜庝换鎰弜鈭圛锛岄兘鏈塮(a+x)=f(a-x)锛屽垯鐩寸嚎x=a灏辨槸鍑芥暟y=f(x)鐨勫绉拌酱锛2銆佸凡鐭(x+a)=f(b-x) 锛屽垯鏈 f((a+b)/2+x)=f((x+b/2-a/2)+a)=f(b-(x+b/2-a/2))=f(b/2+a/2-x)=f((a+b)/2-x)...
绛旓細涓瀹氳娉ㄦ剰~~璇ュ尯闂村繀椤绘槸杩炵画鐨勨︹﹁繖涓獈~姣斿悗闈㈤偅浜涢兘閲嶈
绛旓細璁惧嚱鏁皔=f(x)鐨勫畾涔夊煙涓篒,濡傛灉瀵逛簬瀹氫箟鍩烮鍐呯殑鏌愪釜鍖洪棿D鍐呯殑浠绘剰涓や釜鑷彉閲弜1,x2,褰搙1 濡傛灉瀵逛簬鍖洪棿D涓婄殑浠绘剰涓や釜鑷彉閲忕殑鍊紉1,x2,褰搙1f(x2),閭ｄ箞灏辫f(x)鍦ㄨ繖涓尯闂翠笂鏄噺鍑芥暟.鍖洪棿D绉颁负y=f(x)鐨勫崟璋冨噺鍖洪棿. 娉ㄦ剰:鍑芥暟鐨勫崟璋冩ф槸鍑芥暟鐨勫眬閮ㄦц川; (2) 鍥捐薄鐨勭壒鐐 濡傛灉鍑芥暟y=f(x)鍦ㄦ煇涓尯闂...
绛旓細涓嶆槸鎵鏈夌殑鍑芥暟閮芥湁瀵兼暟锛屼竴涓嚱鏁颁篃涓嶄竴瀹氬湪鎵鏈夌殑鐐逛笂閮芥湁瀵兼暟銆傝嫢鏌愬嚱鏁板湪鏌愪竴鐐瑰鏁板瓨鍦紝鍒欑О鍏跺湪杩欎竴鐐瑰彲瀵硷紝鍚﹀垯绉颁负涓嶅彲瀵笺傜劧鑰岋紝鍙鐨勫嚱鏁颁竴瀹氳繛缁紱涓嶈繛缁殑鍑芥暟涓瀹氫笉鍙銆傚浜庡彲瀵肩殑鍑芥暟f(x)锛寈↦f'(x)涔熸槸涓涓嚱鏁帮紝绉颁綔f(x)鐨瀵煎嚱鏁帮紙绠绉板鏁帮級銆傚鎵惧凡鐭ョ殑鍑芥暟鍦ㄦ煇鐐...
