题目

设函数f（x）=（ax+b）ex，g（x）=﹣x2+cx+d．若函数f（x）和g（x）的图象都过点P（0，1），且在点P处有相同的切线y=2x+1． （I）求a，b，c，d的值； （Ⅱ）当x∈[0，+∞）时，判断函数h（x）=f（x）﹣g（x）的单调性． 答案：【考点】导数的运算． 【分析】（Ⅰ）对f（x），g（x）进行求导，已知在交点处有相同的切线及曲线y=f（x）和曲线y=g（x）都过点P（0，1），从而解出a，b，c，d的值； （Ⅱ）对函数h（x）=f（x）﹣g（x）进行求导，即可判断其单调性． 【解答】解：（Ⅰ）f′（x）=（ax+a+b）ex， ∴， ∴a=b=1， g′（x）=(2013·高考广东卷，D)While Jennifer was at home taking an online exam for her business law class，a monitor(监控器)a few hundred miles away was watching her every move.Using a web camera equipped in Jennifer’s Los Angeles apartment，the monitor in Phoenix tracked how frequently her eyes moved from the computer screen and listened for the secret sounds of a possible helper in the room.Her Internet access was locked－remotely－to prevent Internet searches，and her typing style was analyzed to make sure she was who she said she was：Did she enter her student number at the same speed as she had in the past? Or was she slowing down?In the battle against cheating，this is the cutting_edge and a key to encourage honesty in the booming field of online education.The technology gives trust to the entire system，to the institution and to online education in general.Only with solid measures against cheating，experts say，can Internet universities show that their exams and diplomas are valid—that students haven’t just searched the Internet to get the right answers.Although online classes have existed for more than a decade，the concern over cheating has become sharper in the last year with the growth of“open online courses.”Private colleges，public universities and corporations are jumping into the online education field.spending millions of dollars to attract potential students，while also taking steps to help guarantee honesty at a distance.Aside from the web cameras，a number of other high?tech methods are becoming increasingly popular.Among them are programs that check students’ identities using personal information，such as the telephone numbers they once used.Other programs can produce unique exams by drawing on a large list of questions and can recognize possible cheaters by analyzing whether difficult test questions are answered at the same speed as easy ones.As in many university classes，term papers are scanned against some large Internet data banks for cheating.1.Why was Jennifer watched in an online exam?A．To correct her typing mistakes.B．To find her secrets in the room.C．To prevent her from slowing down.D．To keep her from dishonest behaviors.2.The underlined expression cutting edge in Paragraph 3 is closest in meaning to________.A．advanced techniqueB．sharpening toolC．effective ruleD．dividing line 3.For Internet universities，exams and diplomas will be valid if________.A．they can attract potential studentsB．they can defeat academic cheatingC．they offer students online helpD．they offer many online courses4.Some programs can find out possible cheaters by________.A．checking the question answering speedB．producing a large number of questionsC．scanning the Internet test questionsD．giving difficult test questions5.Which of the following is the best title of this passage?A．The Advantages of Online ExamsB．The High?tech Methods in Online CoursesC．The Fight against Cheating in Online EducationD．The War against the Booming of Online Education