高数老师们，这道题怎么看出f'(0)=0?
\u8fd9\u662f\u9ad8\u6570\u4e2d\u7684\u4e00\u9053\u9898\uff0c\u8bf7\u95ee\u8001\u5e08\u8be5\u600e\u4e48\u505a\u5462\uff1f
\u4f46\u6ce8\u610f\u5230\u7b49\u53f7\u4e0d\u80fd\u6210\u7acb\uff0c\u5373\u6709\u4e25\u683c\u4e0d\u7b49\u53f7\u6210\u7acb
\u7b54\u6848\u662f\uff1a37-40BAAD 41-45 AADCD 46-50 ADCDB
诺一次，为保证0/0型，得f'(0)=0绛旓細璇轰竴娆★紝涓轰繚璇0/0鍨嬶紝寰f'(0)=0
绛旓細鍙绉垎鏈夋剰涔夛紝涔熷氨鏄绉嚱鏁板彲绉紝閭ｄ箞鍘熷嚱鏁板氨鏄繛缁殑
绛旓細鍙互杩欐牱鐪嬶紝濡傛灉x瓒嬪悜浜0锛岄偅椤朵笂鐨刦(x)涔熻秼杩0锛岄偅灏辨槸0姣0鍨锛岀粨鏋滄槸涓嶇‘瀹氱殑锛屼絾鍙宠竟涔熸槸0姣0鍨嬶紝涓や釜鏁伴兘涓嶇‘瀹氾紝鎵浠ュ拰鏄笉纭畾鐨勩傚鏋渇(x)涓嶄负0锛岄偅涔堝乏杈筬(x)/x鐨勭粨鏋滀负鏃犵┓澶э紝浣嗗彸杈规槸0姣0锛屽彲鑳芥槸鏃犵┓灏忋佹棤绌峰ぇ锛屾垨鑰呬竴涓‘瀹氱殑鏁帮紝褰撶劧鏍规嵁棰樻剰鍙兘鏄棤绌峰ぇ銆傚畠浠殑鍜屼篃...
绛旓細閫塀
绛旓細瑕佹湁涓绉嶆暣浣撹蹇碉紝鐔熺粌搴旂敤鍏紡锛屽寲瑙ｆ垚绠鍗曠殑绠楁硶鎴栬呴傚悎鑷繁鐨勭畻娉曘傝鍒嗘竻f(x)鍜寈鐨勫叧绯诲拰鍖哄埆銆f(x)鏄竴绉嶈繍绠楀叧绯伙紝x鏄湭鐭ユ暟銆傚湪f(f(x))杩欓噷锛宖(x)杩欎釜鏁翠綋灏卞彉鎴愪簡鏈煡鏁帮紝f(f(x))灏辨槸杩愮畻鍏崇郴銆傛悶娓呮杩欑鍏崇郴鐨勮瘽锛宖(f(f(x)))绛夌瓑閮藉彧鏄绠楁妧宸х殑闂浜 ...
绛旓細浣犱笉鎳傜殑鏄粈涔堬紵杩欓噷鐨f'(0)鏄竴涓父鏁 閭ｄ箞瀵筬'(0)x绉垎 寰楀埌鐨勫綋鐒舵槸f'(0)x² /2 閭ｄ箞浠ｅ叆浜掍负鐩稿弽鏁扮殑涓婁笅闄恆鍜-a锛岃繖涓椤逛唬鍏ュ氨鏄0 瀹為檯涓婃兂鐫瀵瑰鍑芥暟绉垎锛岃屼笖涓婁笅闄愪簰涓虹浉鍙嶆暟 寰楀埌鐨勫畾绉垎涓瀹氫负闆
绛旓細鎮ㄥソ锛氭纭殑锛屽彉涓婇檺绉垎姹傚灏辨槸閲岄潰閭ｄ釜鍑芥暟锛岀洿鎺ユ眰闆剁偣灏辨槸鏋佸肩偣浜嗭紝鐒跺悗鏄剧劧0宸﹁竟瀵兼暟灏忎簬0锛屽彸杈瑰ぇ浜0锛屽氨鏄瀬灏忓硷紝甯﹀洖x=0鏃舵眰寰f(0)=0銆傚鏋滃浣犳湁甯姪锛岃閲囩撼锛
绛旓細鍒F(0)=f(0), F(1)=f(1)-1 鍥犱负0<f(x)<1 鍒欙細f(0)>0, f(1)-1<0 鍒橣(0)*F(1)<0 鐢遍浂鐐瑰畾鐞嗭紝蹇呭瓨鍦▁鈭(0,1)浣垮緱F(x)=0锛屽嵆f(x)=x 鑰孎'(x)=f'(x)-1 鍥犱负f(x)鍙锛屼笖f'(x)鈮1,鍒 f'(x)>0鎴栬<0 鍗矲(x)鍦▁鈭(0,...
绛旓細浣犲ソ锛佺涓涓姞鍙峰氨鏄妸 2^x +3^x -2 鍒嗘垚浜 (2^x -1)+(3^x -1)鍥犱负涓ら儴鍒嗘瀬闄愰兘瀛樺湪锛屾墍浠ュ彲浠ュ垎鎴愪袱涓瀬闄愮浉鍔 鐒跺悗鐢ㄧ瓑浠锋棤绌峰皬 e^x -1 ~ x 2^x -1 = e^(x*ln2) -1 ~ x*ln2 3^x -1 = e^(x*ln3) - 1 ~ x*ln3 浠ｈ繘鍘诲氨寰楀埌鍚庨潰鐨勫紡瀛 lna + lnb = ln...
绛旓細f(0-0)=琛ㄧずf锛坸锛夊湪0鐐圭殑宸︽瀬闄愬硷紱鍚屾牱銆俧锛0+0锛夎〃绀哄彸鏋侀檺鍊硷紱鍥犱负鏋侀檺e^x(x瓒嬩簬-鏃犵┓锛=0锛屾墍浠锛0-0锛=-1/1=-1;鍥犱负鏋侀檺e^x(x瓒嬩簬姝ｆ棤绌凤級=姝ｆ棤绌凤紝鎵浠锛0+0锛=1.锛堣繖閲岃繍鐢ㄤ竴娆＄綏蹇呭娉曞垯锛夊笇鏈涜兘甯埌浣犱簡銆傘傘
