Bài tập cuối chương I. ỨNG DỤNG ĐẠO HÀM

Home Lớp 12 Toán lớp 12 - Sách Kết nối tri thức Bài tập cuối chương I. ỨNG DỤNG ĐẠO HÀM ĐỂ KHẢO SÁT VÀ VẼ ĐỒ THỊ HÀM SỐ.Bài tập trung bình

{"common":{"save":0,"post_id":"7549","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5517","post_id":"7549","mon_id":"1159285","chapter_id":"1159288","question":"Cho hàm s\u1ed1 $y=f(x)$<\/span> có \u0111\u1ea1o hàm là $f^\\prime(x)=x^2(2x-1)^2(x+1)$<\/span>. S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a hàm s\u1ed1 \u0111ã cho là<\/p>","options":["A.<\/strong> 0","B.<\/strong> 1","C.<\/strong> 2","D.<\/strong> 3"],"correct":"2","level":"2","hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a hàm s\u1ed1 \u0111\u1ea1t c\u1ef1c tr\u1ecb t\u1ea1i \u0111i\u1ec3m $x_0$<\/span> mà \u0111\u1ea1o hàm \u0111\u1ed5i d\u1ea5u t\u1eeb âm “–“ sang d\u01b0\u01a1ng “+” ho\u1eb7c t\u1eeb d\u01b0\u01a1ng “+” sang âm “–“ .<\/p>","answer":"Ch\u1ecdn B.<\/strong> 1<\/span><\/p>Ta có b\u1ea3ng bi\u1ebfn thiên:<\/p><svg height=\"200\" width=\"320\"> <g><title><\/title><rect fill=\"#fff\" height=\"202\" id=\"canvas_background\" width=\"322\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_14\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"29\" x2=\"28.89999\" y1=\"-1.15\" y2=\"199.84999\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"-1.10001\" x2=\"317.89998\" y1=\"51.85\" y2=\"51.85\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"-1.10001\" x2=\"317.89998\" y1=\"89.85\" y2=\"89.85\"><\/line> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_4\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"9.89999\" xml:space=\"preserve\" y=\"25.85\">x<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_5\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"7.89999\" xml:space=\"preserve\" y=\"73.84999\">y'<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_6\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"7.89999\" xml:space=\"preserve\" y=\"135.84999\">y<\/text> <g id=\"svg_9\"> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" id=\"svg_7\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 51.89999389648438,19.44999313354492) \" x=\"45.89999\" xml:space=\"preserve\" y=\"27.85\">8<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.7506660223007202,0,0,1,-27.69957164119478,0) \" x=\"33.47272\" xml:space=\"preserve\" y=\"24.85\">-<\/text> <\/g> <g id=\"svg_17\"> <g id=\"svg_15\"> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" id=\"svg_13\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 307.89999389648443,20.449993133544897) \" x=\"301.89999\" xml:space=\"preserve\" y=\"28.85\">8<\/text> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_16\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"284.89999\" xml:space=\"preserve\" y=\"28.85\">+<\/text> <\/g> <g id=\"svg_21\"> <g id=\"svg_19\"> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" id=\"svg_18\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 53.89999389648438,105.44998931884766) \" x=\"47.89999\" xml:space=\"preserve\" y=\"113.85\">8<\/text> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_20\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"30.89999\" xml:space=\"preserve\" y=\"113.85\">+<\/text> <\/g> <g id=\"svg_25\"> <g id=\"svg_23\"> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" id=\"svg_22\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 303.89999389648443,102.44998931884764) \" x=\"297.89999\" xml:space=\"preserve\" y=\"110.85\">8<\/text> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_24\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"280.89999\" xml:space=\"preserve\" y=\"110.85\">+<\/text> <\/g> <g id=\"svg_10\"> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_26\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"109.89999\" xml:space=\"preserve\" y=\"24.85\">1<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_27\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.7423241138458252,0,0,1,-67.47725175431515,0) \" x=\"94.91762\" xml:space=\"preserve\" y=\"24.85\">-<\/text> <\/g> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_11\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"160.89999\" xml:space=\"preserve\" y=\"24.85\">0<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_31\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"107.89999\" xml:space=\"preserve\" y=\"76.84999\">0<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_32\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"160.89999\" xml:space=\"preserve\" y=\"76.84999\">0<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_33\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"225.89999\" xml:space=\"preserve\" y=\"76.84999\">0<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_34\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.900437831878662,0,0,1,-64.74147461623943,0) \" x=\"71.89999\" xml:space=\"preserve\" y=\"74.84999\">-<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_36\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"131.89999\" xml:space=\"preserve\" y=\"77.84999\">+<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_37\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"189.89999\" xml:space=\"preserve\" y=\"77.84999\">+<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_38\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"250.89999\" xml:space=\"preserve\" y=\"77.84999\">+<\/text> <g id=\"svg_35\"> <g id=\"svg_29\"> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_12\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"228.89999\" xml:space=\"preserve\" y=\"18.85\">1<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_28\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"228.89999\" xml:space=\"preserve\" y=\"41.84999\">2<\/text> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_30\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"225.89999\" x2=\"243.89999\" y1=\"23.85\" y2=\"24\"><\/line> <\/g> <g id=\"svg_41\" transform=\"rotate(57.68338394165039 78.39999389648432,150.04998779296878) \"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_39\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"34.89999\" x2=\"118.89999\" y1=\"150.84999\" y2=\"151\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_40\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"109.89999\" xml:space=\"preserve\" y=\"156.84999\">><\/text> <\/g> <g id=\"svg_44\" stroke=\"null\" transform=\"rotate(-29.111011505126953 201.11785888671872,147.27377319335938) \"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_42\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"124.27144\" x2=\"273.22897\" y1=\"147.94254\" y2=\"148.09255\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_43\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.773304017945051,0,0,1,-93.64310823930049,-14.40333080291748) \" x=\"197.88617\" xml:space=\"preserve\" y=\"168.34587\">><\/text> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" id=\"svg_45\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"107.89999\" xml:space=\"preserve\" y=\"186.84999\">1<\/text> <\/g> <\/svg><\/span><\/p>D\u1ef1a vào b\u1ea3ng bi\u1ebfn thiên, hàm s\u1ed1 \u0111ã cho có 1 c\u1ef1c tr\u1ecb.<\/p>","type":"choose","extra_type":"shape1","user_id":"131","test":"0","date":"2024-08-25 03:29:54","option_type":"txt","len":0},{"id":"5518","post_id":"7549","mon_id":"1159285","chapter_id":"1159288","question":"\u0110\u1ed3 th\u1ecb hàm s\u1ed1 $y=\\dfrac{x^2-3x}{x^2-6x+9}$<\/span> có bao nhiêu \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn?<\/p>","options":["A.<\/strong> 2","B.<\/strong> 3","C.<\/strong> 0","D.<\/strong> 1"],"correct":"1","level":"2","hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a các \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn.<\/p>","answer":"Ch\u1ecdn A.<\/strong> 2<\/span><\/p>TX\u0110: D = R \\ {3}.<\/p>Ta có: $\\lim_\\limits{x\\to+\\infty}y=1$<\/span> nên \u0111\u1ed3 th\u1ecb có 1 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang là y = 1.<\/p>Và $\\begin{cases}\\lim_\\limits{x\\to3^+}y=+\\infty\\\\\\lim_\\limits{x\\to3^-}y=-\\infty\\end{cases}$<\/span> nên \u0111\u1ed3 th\u1ecb có 1 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng là x = 3.<\/p>V\u1eady \u0111\u1ed3 th\u1ecb hàm s\u1ed1 \u0111ã cho có 2 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn.<\/p>","type":"choose","extra_type":"sheep","user_id":"131","test":"0","date":"2024-08-25 03:34:50","option_type":"txt","len":0},{"id":"5519","post_id":"7549","mon_id":"1159285","chapter_id":"1159288","question":"Bi\u1ebft r\u1eb1ng \u0111\u1ed3 th\u1ecb c\u1ee7a hàm s\u1ed1 $y=-x^3+3x^2+5$<\/span> có hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb A và B. Tính \u0111\u1ed9 dài \u0111o\u1ea1n th\u1eb3ng AB.<\/p>","options":["A.<\/strong> $AB=10\\sqrt{2}$<\/span>","B.<\/strong> $AB=2\\sqrt{3}$<\/span>","C.<\/strong> $AB=2\\sqrt{5}$<\/span>","D.<\/strong> $AB=3\\sqrt{2}$<\/span>"],"correct":"3","level":"2","hint":"","answer":"Ch\u1ecdn C.<\/strong> $AB=2\\sqrt{5}$<\/span><\/span><\/p>Xét hàm s\u1ed1 $y=-x^3+3x^2+5$<\/span> có $y^\\prime=-3x^2+6x$<\/span><\/p>Ta có: $y^\\prime=0$<\/span> ⇔ $-3x^2+6x=0$<\/span> ⇔ x = 0 ho\u1eb7c x = 2.<\/p>Suy ra \u0111\u1ed3 th\u1ecb hàm s\u1ed1 có hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb là A(0; 5) và B(2; 9) ⇒ $\\overrightarrow{AB}=(2;4)$<\/span><\/p>V\u1eady \u0111\u1ed9 dài AB là: $AB=\\sqrt{2^2+4^2}=2\\sqrt{5}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-08-25 03:37:42","option_type":"math","len":0}]}