f(x)=x*lnx的函数图像 x/lnx函数图像是什么样的求图
\u51fd\u6570f(x)=lnx-x\u7684\u56fe\u50cf\u7531f'(x)=1/x-1=0\u5f97x=1\uff0c\u4e14x>1\u65f6f'(x)0\uff0c\u6545f(x)=lnx-x\u5728(0,1)\u4e0a\u662f\u589e\u51fd\u6570\uff0cf(x)=lnx-x\u5728(1\uff0c+\u221e)\u4e0a\u662f\u51cf\u51fd\u6570\uff0c\u7ed3\u5408\u5b9a\u4e49\u57df\uff0c\u53ef\u4ee5\u753b\u51faf(x)=lnx-x\u7684\u8349\u56fe\u5982\u56fe\u6240\u793a
\u5982\u4e0b\u56fe\u6240\u793a\uff1a
x\u8d8b\u5411\u4e8e\u65e0\u7a77\uff0cx-lnx\u4e3a\u65e0\u7a77\u5927\u3002
\u8bbey=x-lnx-x/2=x/2-lnx\u3002
\u5219y'=1/2-1/x\uff0c\u6240\u4ee5\u5f53x>2\u65f6\uff0cy\u5355\u8c03\u9012\u589e
\u663e\u7136\u5f53x=e\u65f6y>0\uff0c\u6240\u4ee5\u5f53x>e\u65f6\uff0cx-lnx-x/2>0\u3002
\u5373x-lnx>x/2\u3002
\u800c\u5f53x-->+\u65e0\u7a77\u5927\u65f6\uff0cx/2-->+\u65e0\u7a77\u5927\uff0c\u6545\u6709x-lnx-->+\u65e0\u7a77\u5927\u3002
\u6269\u5c55\u8d44\u6599
\u51fd\u6570\u7684\u7531\u6765
\u4e2d\u6587\u6570\u5b66\u4e66\u4e0a\u4f7f\u7528\u7684\u201c\u51fd\u6570\u201d\u4e00\u8bcd\u662f\u8f6c\u8bd1\u8bcd\u3002\u662f\u6211\u56fd\u6e05\u4ee3\u6570\u5b66\u5bb6\u674e\u5584\u5170\u5728\u7ffb\u8bd1\u300a\u4ee3\u6570\u5b66\u300b\uff081859\u5e74\uff09\u4e00\u4e66\u65f6\uff0c\u628a\u201cfunction\u201d\u8bd1\u6210\u201c\u51fd\u6570\u201d\u7684\u3002
\u4e2d\u56fd\u53e4\u4ee3\u201c\u51fd\u201d\u5b57\u4e0e\u201c\u542b\u201d\u5b57\u901a\u7528\uff0c\u90fd\u6709\u7740\u201c\u5305\u542b\u201d\u7684\u610f\u601d\u3002\u674e\u5584\u5170\u7ed9\u51fa\u7684\u5b9a\u4e49\u662f\uff1a\u201c\u51e1\u5f0f\u4e2d\u542b\u5929\uff0c\u4e3a\u5929\u4e4b\u51fd\u6570\u3002\u201d\u4e2d\u56fd\u53e4\u4ee3\u7528\u5929\u3001\u5730\u3001\u4eba\u3001\u72694\u4e2a\u5b57\u6765\u8868\u793a4\u4e2a\u4e0d\u540c\u7684\u672a\u77e5\u6570\u6216\u53d8\u91cf\u3002\u8fd9\u4e2a\u5b9a\u4e49\u7684\u542b\u4e49\u662f\uff1a\u201c\u51e1\u662f\u516c\u5f0f\u4e2d\u542b\u6709\u53d8\u91cfx\uff0c\u5219\u8be5\u5f0f\u5b50\u53eb\u505ax\u7684\u51fd\u6570\u3002\u201d\u6240\u4ee5\u201c\u51fd\u6570\u201d\u662f\u6307\u516c\u5f0f\u91cc\u542b\u6709\u53d8\u91cf\u7684\u610f\u601d\u3002
\u6211\u4eec\u6240\u8bf4\u7684\u65b9\u7a0b\u7684\u786e\u5207\u5b9a\u4e49\u662f\u6307\u542b\u6709\u672a\u77e5\u6570\u7684\u7b49\u5f0f\u3002\u4f46\u662f\u65b9\u7a0b\u4e00\u8bcd\u5728\u6211\u56fd\u65e9\u671f\u7684\u6570\u5b66\u4e13\u8457\u300a\u4e5d\u7ae0\u7b97\u672f\u300b\u4e2d\uff0c\u610f\u601d\u6307\u7684\u662f\u5305\u542b\u591a\u4e2a\u672a\u77e5\u91cf\u7684\u8054\u7acb\u4e00\u6b21\u65b9\u7a0b\uff0c\u5373\u6240\u8bf4\u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002
注意定义域是正实数，在原点无定义，但是极限是0
你可以用MATLAB绘图的
绛旓細鐢遍鎰忓彲鐭ワ細g(x)=xlnx+(k-x)ln(k-x),鍒檊'(x)=lnx-ln(k-x)=ln(x/(k-x)),浠'(x)=0,鍒檟=k/2,褰0<x<k/2鏃讹紝g'(x)<0锛屾槸鍗曡皟鍑忕殑锛屽綋x>k/2鏃讹紝g'(x)>0g(x)鍗曡皟澧烇紝鎵浠ュ綋x=k/2鏃讹紝g(x)鍙栨渶灏忓硷紝鏈灏忓间负锛歡(k/2)=kln(k/2)
绛旓細瑙
绛旓細y'=lnx+x*1/x=lnx+1=0 x=1/e 瀹氫箟鍩焫>0 0<x<1/e lnx<-1 鎵浠'<0,鍑鍑芥暟 鍚岀悊寰梮>1/e鏄鍑芥暟 鎵浠=1/e鏄瀬灏忓肩偣 杩欐槸鍞竴鐨勬瀬灏忓 鎵浠ヤ篃鏄渶灏忓肩偣 鎵浠ユ渶灏忓=f(1/e)=-1/e
绛旓細鍗硁=f(a/2-m)-f(a/2+m)鏁呮湁n=-{f(a/2+m)-f[a-(a/2+m)]} 鍗矲(a/2+m)=-n 鍥犳鐐筃(a/2+m锛-n锛変篃鍦鍑芥暟鐨勫浘鍍涓娿傛墍浠ワ紝鍑芥暟F(x)鐨勫浘鍍忔槸浠ョ偣P(a/2,0)涓哄绉颁腑蹇冪殑涓績瀵圭О鍥惧舰銆傗憽 褰揳=2鈭2/e鏃 F(x)=f(x)-f(2鈭2/e-x)=xlnx-(2鈭2/e-x)ln(2鈭...
绛旓細lnx鐨勫嚱鏁板浘鍍濡備笅鍥炬墍绀猴細ln涓轰竴涓畻绗︼紝鎰忔濇槸姹傝嚜鐒跺鏁帮紝鍗充互e涓哄簳鐨勫鏁般俥鏄竴涓父鏁帮紝绛変簬2.71828183鈥nx鍙互鐞嗚В涓簂n(x)锛屽嵆浠涓哄簳x鐨勫鏁帮紝涔熷氨鏄眰e鐨勫灏戞鏂圭瓑浜巟銆俵nx=loge^x
绛旓細f'(x)=lnx+1 鐢眆'(x)=0寰梮=1/e 0<x<1/e鏃讹紝f'(x)<0锛寈>1/e鏃讹紝f'(x)>0锛屾墍浠f(x)鐨鍗曡皟閫掑鍖洪棿涓(1/e,+鈭)锛屽崟璋冮掑噺鍖洪棿涓猴紙0锛1/e锛夈
绛旓細f '(x)=lnx+1 ,鏄庢樉鍦,A涓嶅湪鍑芥暟鍥惧儚涓.璁惧垏鐐逛负B锛坅,alna锛,鍒 kAB=(alna-0)/(a+e^-2)=lna+1 ,鍥犳 alna=(a+e^-2)(lna+1)=alna+a+e^-2*lna+e^-2 ,鎵浠,a+e^-2*lna+e^-2=0 .瑙ｅ緱 a=e^-2 ,鎵浠,kAB= -1 ,鍥犳,鎵姹傜殑鍒囩嚎鏂圭▼涓 y=-(x+e^-2),鍗 x...
绛旓細杩欐槸绗﹀悎鍑芥暟姹傚 绛変簬f(x)=x *(lnx)'+(x)' *lnx=x* 1/x+1*lnx=1+lnx 鏈涢噰绾筹紝璋㈣阿銆
绛旓細(1)鍙互姹傚璁＄畻锛f(x)'=lnx+1浠(x)'鐨勫掓暟涓0锛屽垯lnx=-1,x=1/e鎵浠ユ渶灏忓兼槸f(1/e)'=-锛1/e锛(2)xlnx<=x^2-ax+2 鍦▁>0鎭掓垚绔 瑙ｅ嚭a<=(x^2+2-xlnx)/x=x+2/x-lnx鍙︾瓑寮忓彸杈逛负g(x)鐜版眰g(x)鐨勬渶灏忓糶'(x)=1-2/x^2-1/x=(x^2-x-2)/x^2=(x-2)(x...
绛旓細f(x)涓巊(x)鐨勫浘鍍鎭版湁涓涓叕鍏辩偣 鍥犱负閮芥槸鍏夋粦鏇茬嚎 鎵浠ュ湪浜ょ偣澶勪袱鏇茬嚎鍚勮嚜鍒囩嚎鏂滅巼涔熺浉绛 灏辨槸瀵兼暟鐩哥瓑 灏辨槸f'(x0)=g'(x0)灏辨槸lnx0+1=-2x0+a 鈶 杩樻湁f锛坸0)=g(x0)灏辨槸x0lnx0=-x0²+ax0-2 鈶 娑堝幓a锛屽氨鏈墄0²+x0-2=0瑙ｅ緱x0=-2(鑸嶅幓锛夋垨x0=1 鎶...
