常数除以减函数得?常数除以增函数得?增函数除以常数?减函数除以常数? 增函数除以增函数是减函数还是增函数要是一除以增函
\u51cf\u51fd\u6570\u9664\u4ee5\u51cf\u51fd\u6570\uff0c\u589e\u51fd\u6570\u9664\u4ee5\u589e\u51fd\u6570\uff0c\u51cf\u51fd\u6570\u9664\u4ee5\u589e\u51fd\u6570\uff1f\u6c42\u95ee\u4e0d\u786e\u5b9a\u3002
\u4f8b\u5982f(x)=1/x\uff0cg(x)=x
\u5546\u65e2\u6709\u589e\uff0c\u53c8\u6709\u51cf\u3002
\u589e\u51fd\u6570\u9664\u4ee5\u589e\u51fd\u6570
\u65e2\u6709\u53ef\u80fd\u662f\u589e\u51fd\u6570
\u4e5f\u53ef\u80fd\u662f\u51cf\u51fd\u6570
\u800c\u4e00\u9664\u4ee5\u589e\u51fd\u6570\u7684\u8bdd
\u4e00\u5b9a\u662f\u51cf\u51fd\u6570
后两者很显然:增函数除以正(负)常数是增(减)函数。减函数除以正(负)常数是减(增)函数。
前两者很复杂:不仅涉及常数的符号,而且涉及函数的符号。举例
-x单减,1/x分段单减:
2÷(-x)=-2/x,分段单增;2÷(1/x)=2x(x≠0)单增;
-2÷(-x)=2/x,分段单减;-2÷(1/x)=-2x(x≠0)单减。
x^2+x两个单区,常数乘以它以后变为4个单区啊!
绛旓細澧+澧=澧 鍑+鍑=鍑 澧-鍑=澧 鍑-澧=鍑 澧烇紙鍑忥級鍑芥暟鍙湁鐩稿姞鐩稿噺锛屾病鏈夌浉涔樼浉闄 濂+濂=濂 濂-濂=濂 鍋+鍋=鍋 鍋-鍋=鍋 濂*濂=鍋 鍋*鍋=鍋 濂*鍋=濂 鍑芥暟濂囧伓鎬у彧鏈夌浉鍔犵浉鍑忕浉涔 锛屾病鏈夌浉闄
绛旓細鏃犳硶鍒ゆ柇锛屼緥濡俧(x)=x涓澧炲嚱鏁,g(x)=1/x鍦紙璐熸棤绌凤紝0锛夊拰(0锛屾鏃犵┓)閮芥槸鍑忓嚱鏁锛岃宖(x)/g(x)=x^2 鍦紙璐熸棤绌凤紝0锛夋槸鍑忓嚱鏁帮紝鍦(0锛屾鏃犵┓)鏄鍑芥暟 銆傜敱姝ゅ緱鍒,鑻ラ檺瀹歡(x)鐨勫畾涔夊煙鍒嗗埆涓轰负锛堣礋鏃犵┓锛0锛,(0锛屾鏃犵┓),锛堣礋鏃犵┓锛0锛夊苟(0锛屾鏃犵┓),鍒欏緱鍒扮殑f(x)/g(x)...
绛旓細澧鍑芥暟闄や互澧炲嚱鏁 鏃㈡湁鍙兘鏄鍑芥暟 涔熷彲鑳芥槸鍑忓嚱鏁 鑰屼竴闄や互澧炲嚱鏁扮殑璇 涓瀹氭槸鍑忓嚱鏁
绛旓細X鐨勫彇鍊兼槸铏氭暟(x= -b卤鈭歜^2-4ac 鐨勫肩殑鐩稿弽鏁,涔樹笂铏氭暟i,鏁翠釜寮忓瓙闄や互2a) 褰揳>0鏃,鍑芥暟鍦▁= -b/2a澶勫彇寰楁渶灏忓糵(-b/2a)=4ac-b^2/4a;鍦▄x|x<-b/2a}涓婃槸鍑忓嚱鏁,鍦▄x|x>-b/2a}涓婃槸澧炲嚱鏁;鎶涚墿绾跨殑寮鍙e悜涓;鍑芥暟鐨勫煎煙鏄瘂x|x鈮4ac-b^2/4a}鐩稿弽涓嶅彉 褰揵=0鏃,鎶涚墿绾跨殑瀵圭О杞存槸y...
绛旓細璇曢鍒嗘瀽锛氬綋 鏃讹紝鍑芥暟 涓 鍦 閮芥槸澧炲嚱鏁锛屾墍浠 鍦 鍗曡皟閫掑锛屾墍浠ユ湁 锛屼笉婊¤冻棰樻剰锛涘綋 鏃讹紝 鍦 鍗曡皟閫掑锛屾墍浠ユ湁 锛屼篃涓嶆弧瓒抽鎰忥紱褰 鏃讹紝鏍规嵁棰樻剰鍙煡鍑芥暟 鍦 鍗曡皟閫掑噺锛屽湪 鍗曡皟閫掑锛涜浣垮浠绘剰 锛岄兘鏈 锛屽垯椤绘弧瓒 鍗冲彲锛屽嵆椤绘眰瑙d笉绛 锛岃В寰 .
绛旓細鐮旂┒鎺ㄥ箍鍚庣殑鍑芥暟鐨勫崟璋冩э紙鍙』鍐欏嚭缁撹锛屼笉蹇呰瘉鏄庯級锛屽苟姹傚嚱鏁 锛坣鏄鏁存暟锛夊湪鍖洪棿[ 锛2]涓婄殑鏈澶у煎拰鏈灏忓硷紙鍙埄鐢ㄤ綘鐨勭爺绌剁粨璁猴級銆 锛1锛 锛2锛夊嚱鏁板湪 涓婃槸鍑忓嚱鏁锛屽湪 鏄澧炲嚱鏁帮紙3锛夊綋 鎴 鏃讹紝 鍙栧緱鏈澶у 褰搙=1鏃 鍙栧緱鏈灏忓 锛1锛夊嚱鏁 鐨勬渶灏忓兼槸 ...
绛旓細锛堚厾锛 锛庯紙鈪★級 锛 璇曢鍒嗘瀽锛氾紙鈪狅級鈭 鍦ㄥ尯闂 涓婃槸澧炲嚱鏁帮紝鈭村綋 鏃讹紝 鎭掓垚绔嬶紝鍗 鎭掓垚绔嬶紝鎵浠 锛庡張 鍦ㄥ尯闂 涓婃槸鍑忓嚱鏁锛屾晠褰 鏃讹紝 鎭掓垚绔嬶紝鍗 鎭掓垚绔嬶紝鎵浠 锛庣患涓婏紝 锛庣敱 锛屽緱 锛屼护 锛屽垯 锛岃 锛屾墍浠 鐨勫浘璞′笂 澶勭殑鍒囩嚎涓庣洿绾 骞宠锛屾墍浠...
绛旓細澧炲嚱鏁颁箻浠ヤ竴涓鏁版槸澧炲嚱鏁 澧炲嚱鏁颁箻浠ヤ竴涓礋鏁版槸鍑忓嚱鏁 澧炲嚱鏁颁箻浠ヤ竴涓0鏄甯告暟鍑芥暟銆
绛旓細纭畾缁撹銆傦紙3锛夋牴鎹埖c鈭堬紙1,9锛夌劧鍚庡緱鍒板嚱鏁扮殑鍗曡皟鍖洪棿杩涜屽緱鍒版渶鍊艰В. (1) 鐢卞凡鐭ュ緱 ="4," 鈭碽=4.(2)璁 , 鈭 锛屼笖 < 锛 鈭 锛 ,鐢 , 鈭 锛 < 寰0< <1,1- >0锛屾晠 锛 >0 ,浜庢槸 锛 >0,鍗 > .鈭 = 鍦 涓婃槸鍑忓嚱鏁.(3...
绛旓細螖= b^2-4ac锛0鏃讹紝鎶涚墿绾夸笌x杞存病鏈変氦鐐广俋鐨勫彇鍊兼槸铏氭暟锛坸= -b卤鈭歜^2锛4ac 鐨勫肩殑鐩稿弽鏁帮紝涔樹笂铏氭暟i锛屾暣涓紡瀛闄や互2a锛夊綋a>0鏃讹紝鍑芥暟鍦▁= -b/2a澶勫彇寰楁渶灏忓糵(-b/2a)=4ac-b^2/4a锛涘湪{x|x<-b/2a}涓婃槸鍑忓嚱鏁锛屽湪{x|x>-b/2a}涓婃槸澧炲嚱鏁帮紱鎶涚墿绾跨殑寮鍙e悜涓婏紱鍑芥暟鐨勫煎煙...