函数f（x）=xex（其中e=2.71828…）的图象在（ 已知函数f（x）=axlnx图象上点（e，f（e））处的切线...
\u8bbe\u51fd\u6570f\uff08x\uff09=lnx-x2+ax\uff08\u5176\u4e2d\u65e0\u7406\u6570e=2.71828\u2026\uff0ca\u2208R\uff09\uff0e\uff08I\uff09\u82e5\u51fd\u6570f\uff08x\uff09\u5728\uff080\uff0ce]\u4e0a\u4e0d\u662f\u5355\u8c03\u51fd\u6570\uff0c\uff08\u2160\uff09f\u2032(x)\uff1d?2x2+ax+1x=-2x2?ax?1x\uff0c\u8981\u4f7ff\uff08x\uff09\u5728\uff080\uff0ce]\u4e0a\u4e0d\u5355\u8c03\uff0cf'\uff08x\uff09\u5728\uff080\uff0ce\uff09\u5185\u5fc5\u6709\u96f6\u70b9\u4e14\u5728\u96f6\u70b9\u5de6\u53f3\u5f02\u53f7\uff0c\u5373h\uff08x\uff09=2x2-ax-1\u5728\uff080\uff0ce\uff09\u5185\u6709\u96f6\u70b9\u4e14\u5728\u96f6\u70b9\u5de6\u53f3\u5f02\u53f7\uff0e \u56e0\u4e3a\u25b3=a2+8\uff1e0\uff0c\u6240\u4ee5\u65b9\u7a0b2x2-ax-1=0\u6709\u4e24\u4e2a\u4e0d\u7b49\u7684\u5b9e\u6570\u6839x1\uff0cx2\uff0c\u7531\u4e8ex1x2=?12\uff1c0\uff0c\u4e0d\u59a8\u8bbex1\uff1c0\uff0cx2\uff1e0\uff0c\u6240\u4ee5x1\uff1c0\uff0cx2\u2208\uff080\uff0ce\uff09\uff0c\u7531h\uff08x\uff09\u56fe\u8c61\u53ef\u77e5\uff1ah\uff080\uff09h\uff08e\uff09\uff1c0\uff0c\u53732e2-ae-1\uff1e0\uff0c\u89e3\u5f97 a\uff1c2e-1e\uff0e\uff08\u2161\uff09\u56e0\u4e3af\u2032(x0)\uff1d1x0?2x0+a\uff0c\u53c8\u5207\u70b9C\uff08x0\uff0clnx0?x20+ax0\uff09\uff0c\u6240\u4ee5\u5207\u7ebfl\u7684\u65b9\u7a0b\u4e3ay?(lnx0?x20+ax0)\uff1d(1x0?2x0+a)(x?x0)\uff0c\u5373y\uff1d(1x0?2x0+a)x?1+x20+ln?x0\uff0c\uff08x0\u4e3a\u5e38\u6570\uff09\uff0e\u2026\uff088\u5206\uff09\u4ee4g(x)\uff1df(x)?[(1x0?2x0+a)x?1+x20+ln?x0]\uff0c\u5219g\uff08x\uff09=ln?x?x2?[(1x0?2x0)x?1+x20+ln?x0]\uff0c\u5219g\u2032(x)\uff1d1x?2x?(1x0?2x0)=?(x?x0)(2xx0+1xx0)\uff1d?2(x?x<
\uff08I\uff09\u7531\u70b9\uff08e\uff0cf\uff08e\uff09\uff09\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u4e0e\u76f4\u7ebf2x-y=0\u5e73\u884c\uff0c\u5f97\u8be5\u5207\u7ebf\u659c\u7387\u4e3a2\uff0c\u5373f'\uff08e\uff09=2\uff0e\u53c8\u2235f'\uff08x\uff09=a\uff08lnx+1\uff09\uff0c\u4ee4a\uff08lne+1\uff09=2\uff0ca=1\uff0c\u6240\u4ee5f\uff08x\uff09=xlnx\uff0e\uff08II\uff09\u7531\uff08I\uff09\u77e5f'\uff08x\uff09=lnx+1\uff0c\u663e\u7136f'\uff08x\uff09=0\u65f6x=e-1\u5f53x\u2208(0\uff0c1e)\u65f6f'\uff08x\uff09\uff1c0\uff0c\u6240\u4ee5\u51fd\u6570f(x)\u5728(0\uff0c1e)\u4e0a\u5355\u8c03\u9012\u51cf\uff0e\u5f53x\u2208(1e\uff0c+\u221e)\u65f6f'\uff08x\uff09\uff1e0\uff0c\u6240\u4ee5\u51fd\u6570f\uff08x\uff09\u5728(1e\uff0c+\u221e)\u4e0a\u5355\u8c03\u9012\u589e\uff0c\u24601e\u2208[n\uff0cn+2]\u65f6\uff0cf(x)min\uff1df(1e)\uff1d?1e\uff1b\u24611e\u2264n\uff1cn+2\u65f6\uff0c\u51fd\u6570f\uff08x\uff09\u5728[n\uff0cn+2]\u4e0a\u5355\u8c03\u9012\u589e\uff0c\u56e0\u6b64f\uff08x\uff09min=f\uff08n\uff09=nlnn\uff1b\u6240\u4ee5f(x)min\uff1d?1e\uff0c(0\uff1cn\uff1c1e)nlnn\uff0c(n\u22651e)\uff1b\uff08III\uff09\u5bf9\u4e00\u5207x\u2208\uff080\uff0ce]\uff0c3f\uff08x\uff09\u2265g\uff08x\uff09\u6052\u6210\u7acb\uff0c\u53c8g\uff08x\uff09=x2-tx-2\uff0c\u22343xlnx\u2265x2-tx-2\uff0c\u5373t\u2265x?3lnx?2x\uff0e\u8bbeh(x)\uff1dx?3lnx?2x\uff0cx\u2208(0\uff0ce]\uff0c\u5219h\u2032(x)\uff1d1?3x+2x2\uff1dx2?3x+2x2\uff1d(x?1)(x?2)x2\uff0c\u7531h'\uff08x\uff09=0\u5f97x=1\u6216x=2\uff0c\u2234x\u2208\uff080\uff0c1\uff09\uff0ch'\uff08x\uff09\uff1e0\uff0ch\uff08x\uff09\u5355\u8c03\u9012\u589e\uff0cx\u2208\uff081\uff0c2\uff09\uff0ch'\uff08x\uff09\uff1e0\uff0ch\uff08x\uff09\u5355\u8c03\u9012\u51cf\uff0cx\u2208\uff082\uff0ce\uff09\uff0ch'\uff08x\uff09\uff1e0\uff0ch\uff08x\uff09\u5355\u8c03\u9012\u589e\uff0c\u2234h\uff08x\uff09\u6781\u5927\u503c=h\uff081\uff09=-1\uff0c\u4e14h\uff08e\uff09=e-3-2e-1\uff1c-1\uff0c\u6240\u4ee5h\uff08x\uff09max=h\uff081\uff09=-1\uff0e\u56e0\u4e3a\u5bf9\u4e00\u5207x\u2208\uff080\uff0ce]\uff0c3f\uff08x\uff09\u2265g\uff08x\uff09\u6052\u6210\u7acb\uff0c\u2234t\u2265h\uff08x\uff09max=-1\uff0e\u6545\u5b9e\u6570t\u7684\u53d6\u503c\u8303\u56f4\u4e3a[-1\uff0c+\u221e\uff09\uff0e
∵f（x）=xex，∴f′（x）=x（ex）′+x′ex=ex（x+1）
∴f′（0）=1，f（0）=0
即函数f（x）图象在点（0，0）处的切线斜率为1
∴图象在点（0，f（0））处的切线方程为x-y=0
故答案为x-y=0．
绛旓細鈭礷锛坸锛=xex锛屸埓f鈥诧紙x锛=x锛坋x锛夆+x鈥瞖x=ex锛坸+1锛夆埓f鈥诧紙0锛=1锛宖锛0锛=0鍗鍑芥暟f锛坸锛鍥捐薄鍦ㄧ偣锛0锛0锛夊鐨勫垏绾挎枩鐜囦负1鈭村浘璞″湪鐐癸紙0锛宖锛0锛夛級澶勭殑鍒囩嚎鏂圭▼涓簒-y=0鏁呯瓟妗堜负x-y=0锛
绛旓細锛1锛夆埖f锛坸锛=xex鈭磃鈥诧紙x锛=ex+xex锛屸埓f鈥诧紙1锛=2e锛屽張f锛1锛=e锛屸埓鏇茬嚎y=f锛坸锛夊湪鐐癸紙1锛宖锛1锛夛級澶勭殑鍒囩嚎鏂圭▼涓簓-e=2e锛坸-1锛夛紝鍗2ex-y-e=0锛庯紙2锛夆埖浠绘剰x鈭圧锛宖锛坸锛夛紴m鎭掓垚绔嬶紝鈭村彧瑕乫锛坸锛塵in锛瀖鍗冲彲锛屼护f鈥诧紙x锛夛紴0?x锛-1锛屽嵆鍑芥暟f锛坸锛鐨勫崟璋冮掑鍖洪棿鏄...
绛旓細f(x)=xe^x f'(x)=e^x+xe^x=e^x(1+x)褰搙<-1鏃讹紝f'(x)<0 褰搙>-1鏃讹紝f'(x)>0 鎵浠ワ紙-00锛-1锛夋槸鍗曡皟鍑忓尯闂 锛-1锛+00锛夋槸鍗曡皟澧炲尯闂 鍒╃敤瀵兼暟绗﹀彿鍒ゅ畾鍗曡皟鎬
绛旓細鍏堟眰瀵硷紝fx鈥=e^x+xe^x 褰搙=1鏃讹紝f锛1)'=2e,鍗冲垏绾挎枩鐜噆=2e x=1鏃讹紝f锛1锛=e锛屽垏绾胯繃鐐癸紙1锛宔锛夊垏绾挎柟绋嬩负y-e=2e锛坸-1)y=2ex-e
绛旓細瑙ｇ瓟锛氳В锛鍑芥暟鐨勫鏁颁负f'锛坸锛=ex+xex锛屽垯f'锛1锛=e+e=2e锛屽嵆鍒囩嚎鏂滅巼k=f'锛1锛=2e锛屽張f锛1锛=e锛屽嵆鍒囩偣鍧愭爣涓猴紙1锛宔锛夛紟鎵浠ュ垏绾挎柟绋嬩负y-e=2e锛坸-1锛夛紝鍗冲垏绾挎柟绋嬩负2ex-y-e=0锛庢晠閫堿锛庣偣璇勶細鏈涓昏鑰冩煡瀵兼暟鐨勫嚑浣曟剰涔変互鍙婂垏绾挎柟绋嬬殑姹傛硶锛屾瘮杈冨熀纭锛
绛旓細瑙ｉ鎬濊矾锛氱敱棰樻剰锛屽彲鍏堟眰鍑篺鈥诧紙x锛=锛坸+1锛塭 x锛屽埄鐢ㄥ鏁扮爺绌跺嚭鍑芥暟鐨勫崟璋冩э紝鍗冲彲寰楀嚭x=-1涓篺锛坸锛夌殑鏋佸皬鍊肩偣 鐢变簬f锛坸锛=xex锛屽彲寰梖鈥诧紙x锛=锛坸+1锛塭x锛屼护f鈥诧紙x锛=锛坸+1锛塭x=0鍙緱x=-1 浠鈥诧紙x锛=锛坸+1锛塭x锛0鍙緱x锛-1锛屽嵆鍑芥暟鍦紙-1锛+鈭烇級涓婃槸澧炲嚱鏁 浠鈥...
绛旓細姹傚f鈥锛坸锛=锛x+1锛塭^x 浠鈥橈紙x锛=0锛岃В寰梮=-1 褰搙>-1鏃讹紝f鈥橈紙x锛>0 f(x)鍗曡皟閫掑 褰搙<-1鏃讹紝f鈥橈紙x锛<o f(x)鍗曡皟閫掑噺 鎵浠(x)鐨勫崟璋冨鍖洪棿涓猴紙-1锛屾鏃犵┓锛夛紝鍑忓尯闂翠负锛堣礋鏃犵┓锛-1锛夋槸鎴戣嚜宸卞仛鐨勫晩锛屼笉涓瀹氬锛屽垰濂芥槸杩欐鍋囨湡浣滀笟锛屽氨椤烘墜缁欎綘鎵撲笂浜嗭紝甯屾湜鑳...
绛旓細f鈥(x)=锛x+1锛塭x 浠ゅ鍑芥暟涓洪浂姹傚緱x=-1 f锛坸锛鐨勬瀬鍊兼槸f锛-1锛=-1/e
绛旓細鐢眣鈥=1x鐭鈥瞸x=x0=1x0鐢卞凡鐭ユ潯浠:ln x0x0=1x0,瑙ｅ緱x0=e,k=1e.绛旀C3.宸茬煡鍑芥暟f(x)=ax2+3x-2鍦ㄧ偣(2,f(2))澶勭殑鍒囩嚎鏂滅巼涓7,鍒欏疄鏁癮鐨勫间负A.-1 B.1 C.卤1 D.-23.B [鍥犱负f鈥(x)=2ax+3,鎵浠ョ敱棰樻剰寰2a脳2+3=7,瑙ｅ緱a=1.鏁呴塀.]4.宸茬煡鍑芥暟f(x)=xex,鍒檉鈥(x)=_...
绛旓細鐢ㄦ眰瀵兼柟娉曪紝鍦ㄨ礋鏃犵┓鍒拌礋1鍗曡皟閫掑噺锛岃礋1鍒版鏃犵┓鍗曞噵閫掑锛屾瀬灏忓0锛屾棤鏋佸ぇ鍊
