函数f(x)=lnx/x^2的图像？ 函数f(x)=lnx-x^2/2的大致图像
\u51fd\u6570f(x)=lnx/x^2\u7684\u56fe\u50cf\uff1f
\u5982\u56fe
\u73b0\u5bf9\u5176\u6c42\u5bfc\uff0cf'\uff08x\uff09=\uff081-x^2\uff09/x\u3010x\uff1e0\u3011
\u5f53f'\uff08x\uff09=0\u65f6\uff0c\u5f97\u5230x=\u00b11
\u5f53X\u2208\uff080,1\uff09\u65f6\uff0cf\uff08x\uff09\u5355\u8c03\u9012\u589e\u3002X\u2208\uff081,\u6b63\u65e0\u7a77\uff09\u65f6\uff0cf\uff08x\uff09\u5355\u8c03\u9012\u51cf
\u6240\u4ee5\u5f53x=1\u65f6\uff0cf\uff08x\uff09\u53d6\u5230\u6700\u5927\u503c\uff0cf\uff081\uff09= -1/2
\u6240\u4ee5\u56fe\u8c61\u5e94\u8be5\u5927\u81f4\u662f
\u56fe\u753b\u7684\u4e0d\u662f\u5f88\u597d\uff0c\u51d1\u548c\u7740\u770b\u5427
\u671b\u91c7\u7eb3\uff0cO(\u2229_\u2229)O\u8c22\u8c22
利用单调性凹凸性、渐近线及与坐标轴交点即可画出图像。
绛旓細f(x)=lnx鐨勫師鍑芥暟鏄疐(x)=xlnx-x+C銆傞鍏堬紝鎴戜滑闇瑕佹壘鍒癴(x)=lnx鐨勫師鍑芥暟锛屼篃灏辨槸姹傚叾涓嶅畾绉垎銆備娇鐢ㄥ垎閮ㄧН鍒嗘硶锛屾垜浠护u=lnx锛宒v=dx锛屽垯du=dx/x锛寁=x銆傚洜姝わ紝鍘熷嚱鏁癋(x)鍙互琛ㄧず涓猴細F(x) = xlnx - ∫xd(lnx)= xlnx - ∫x*(1/x)dx = xlnx - ∫dx = xlnx...
绛旓細f(x)=lnx鐨鍑芥暟鍥惧儚鏄竴鏉¤繃I锛孖V璞￠檺鐨勫鏁板嚱鏁版洸绾匡紝鏄竴鏉″畾涔夊煙鍦(0,+鈭)锛屽煎煙鍦≧涓婏紝鍗曡皟閫掑鐨勬洸绾裤傛洸绾跨粡杩(1,0)锛屼笖鍚戜笂鍑歌捣銆俵nx鐨勬ц川锛1銆佸畾涔夊煙涓簒鈭(0,+鈭)锛屽煎煙涓(-鈭,+鈭)锛屽浘褰㈠垎甯冨湪涓鍥涜薄闄愶紱涓哄崟璋冮掑锛岄潪濂囬潪鍋躲2銆佷粠瀵兼暟鏉ョ湅鍗曡皟鎬х湅璧锋潵鏇村揩y'=lnx-1锛/...
绛旓細瀵规暟鍑芥暟濡俧=lnx锛屽叾瀹氫箟鍩熸槸鎵鏈夋瀹炴暟銆傝繖鏄洜涓哄鏁板嚱鏁扮殑瀹氫箟鏄熀浜庢鏁扮殑骞傝繍绠楋紝瀹冮渶瑕佽緭鍏ヤ竴涓鏁版潵璁＄畻杈撳嚭鍊笺傛崲鍙ヨ瘽璇达紝lnx鏄鏁板嚱鏁扮殑鍩烘湰褰㈠紡锛屽畠鐨勮嚜鍙橀噺x蹇呴』澶т簬闆讹紝鍚﹀垯瀵规暟杩愮畻娌℃湁鎰忎箟銆備簩銆乫=lnx鐨勭壒鐐 瀵逛簬鍑芥暟f=lnx鏉ヨ锛屽彧鏈夊湪杈撳叆鍊煎ぇ浜庨浂鐨勬儏鍐典笅锛屽嚱鏁版墠鏈夋槑纭殑杈撳嚭鍊笺...
绛旓細鍦ㄦ暟瀛︿腑锛屽浜庡嚱鏁 y = f(x)锛屽叾瀵兼暟 y' = f'(x) 琛ㄧず y 鍦 x 澶勭殑鍒囩嚎鏂滅巼銆傚亣璁鍑芥暟 f(x) = lnx锛屾垜浠鎵惧嚭 f'(x)銆傛牴鎹鏁板嚱鏁扮殑姹傚瑙勫垯锛屾垜浠煡閬擄細(ln(x))' = 1/x 杩欎釜鍏紡鍛婅瘔鎴戜滑 lnx 鐨勫鏁版槸澶氬皯銆傝绠楃粨鏋滀负锛歠'(x) = 0 鎵浠ワ紝鍑芥暟 f(x) = lnx 鐨勫鏁版槸 ...
绛旓細x鈫0+锛f(x)=lnx鈫-鈭烇紝杩欐椂f(x)鏄礋鏃犵┓澶с倄鈫+鈭烇紝f(x)=lnx鈫+鈭烇紝杩欐椂f(x)鏄鏃犵┓澶с備互涓嬫槸鏃犵┓澶х殑鐩稿叧浠嬬粛锛氬湪闆嗗悎璁轰腑瀵规棤绌锋湁涓嶅悓鐨勫畾涔夈傚痉鍥芥暟瀛﹀搴锋墭灏旀彁鍑猴紝瀵瑰簲浜庝笉鍚屾棤绌烽泦鍚堢殑鍏冪礌鐨勪釜鏁帮紙鍩烘暟锛夛紝鏈変笉鍚岀殑鈥滄棤绌封濄備袱涓棤绌峰ぇ閲忎箣鍜屼笉涓瀹氭槸鏃犵┓澶э紝鏈夌晫閲忎笌鏃犵┓...
绛旓細杩欎釜涓嶄竴瀹氱殑锛屽垎鎯呭喌鑰屽畾 濡傚鏁鍑芥暟F(x)=lnx锛屽垯鍏跺畾涔夊煙涓(0,姝ｆ棤绌峰ぇ)锛屾绉嶈娉曟槑纭寚鏄庝簡F(x)鏄寚鏁板嚱鏁 濡傛灉棰樼洰涓彧璇村嚱鏁癋(x)=lnx锛屽垯濂囧畾涔夊煙涓哄彲浠ユ槸(0,姝ｆ棤绌峰ぇ)鐨勪换鎰忎竴涓瓙鍖洪棿锛屼緥濡(0,8),(0,8]绛
绛旓細lnx 琛ㄧず x 鐨勮嚜鐒跺鏁般俧(x) 琛ㄧず瀵瑰簲鐨鍑芥暟鍊笺傝礋鏁颁笌0鏃犲鏁帮紝鑷彉閲 x 涓 澶т簬0 鐨勫疄鏁般1鐨勫鏁版案涓0銆俧(x) 鐨勮寖鍥存槸璐熸棤绌峰埌姝ｆ棤绌枫倄灏忎簬1锛屽鏁颁负璐燂紝x澶т簬1锛屽鏁颁负姝ｃf(x)=lnx 鏄粠璐熸棤绌 鍒 姝ｆ棤绌 鐨勫嚱鏁般
绛旓細褰搉鈮-1鏃 鈭玿^indx=1/(n+1)*x^(n+1)+C 褰搉=-1鏃 鈭玿^ndx=lnx+C
绛旓細瀹氫箟鍩焫>0 f(x)=lnx f'(x)=1/x>0 鍑芥暟f(x)=lnx鏄崟璋冨鍑芥暟 鍗曡皟澧炲尯闂达細(0,+鈭)
绛旓細鍥犱负f(x)鐨勫畾涔夊煙鏄痆1,2]鎵浠nx鐨勫彇鍊艰寖鍥存槸[1,2]鎵浠ヨВ1<=lnx<=2 灏卞彲浠ュ緱鍒癴(lnx)鐨勫畾涔夊煙涓猴細e<=x<=e^2(e鐨勫钩鏂)
