Khảo sát sự biến thiên và vẽ đồ thị của hàm số

Home Lớp 12 Toán lớp 12 - Sách Kết nối tri thức Bài 4. Khảo sát sự biến thiên và vẽ đồ thị của hàm số.Bài tập trung bình

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\" y=\"2\"><\/image> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> a > 0, d > 0","B.<\/strong> a < 0, d > 0","C.<\/strong> a > 0, d < 0","D.<\/strong> a < 0, d < 0"],"correct":"4","level":"2","hint":"S\u1eed d\u1ee5ng \u0111\u1ed3 th\u1ecb hàm s\u1ed1 b\u1eadc 3.<\/p>","answer":"Ch\u1ecdn D.<\/strong> a < 0, d < 0.<\/span><\/p>Ta có $\\displaystyle\\lim_{x\\to+\\infty}y=-\\infty$<\/span> ⇒ \u0111\u1ed3 th\u1ecb nhánh ngoài cùng c\u1ee7a hàm s\u1ed1 h\u01b0\u1edbng \u0111i xu\u1ed1ng nên h\u1ec7 s\u1ed1 a < 0<\/strong>. Giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb hàm s\u1ed1 v\u1edbi tr\u1ee5c tung Oy là \u0111i\u1ec3m n\u1eb1m bên d\u01b0\u1edbi tr\u1ee5c hoành nên khi x = 0 thì y = d < 0<\/strong>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-07-07 01:24:52","option_type":"txt","len":2},{"id":"5426","post_id":"7532","mon_id":"1159285","chapter_id":"1159288","question":"Cho hàm s\u1ed1 $f(x)=\\dfrac{ax+1}{bx+c}$<\/span>, v\u1edbi a, b, c ∈ R có b\u1ea3ng bi\u1ebfn thiên nh\u01b0 sau. Trong các s\u1ed1 a, b và c có bao nhiêu s\u1ed1 d\u01b0\u01a1ng?<\/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\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" 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=\"0.5\" x2=\"320.5\" y1=\"36.25\" y2=\"36\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"0.5\" x2=\"320.5\" y1=\"81.25\" y2=\"81\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"45.5\" x2=\"46\" y1=\"0.25\" y2=\"201.25\"><\/line> <line fill=\"none\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"183.5\" x2=\"184\" y1=\"36.25\" y2=\"201.25\"><\/line> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-style=\"italic\" font-weight=\"bold\" id=\"svg_5\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"13.5\" xml:space=\"preserve\" y=\"26.25\">x<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-style=\"italic\" font-weight=\"bold\" id=\"svg_6\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.5\" xml:space=\"preserve\" y=\"66.25\">f '(x)<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-style=\"italic\" font-weight=\"bold\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"6.5\" xml:space=\"preserve\" y=\"145.25\">f(x)<\/text> <g id=\"svg_10\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"49.5\" xml:space=\"preserve\" y=\"16.25\">_<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 67.50000000000001,20.249999999999996) \" x=\"62.5\" xml:space=\"preserve\" y=\"27.25\">8<\/text> <\/g> <g id=\"svg_13\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"188.5\" xml:space=\"preserve\" y=\"187.25\">_<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 206.50000000000003,191.25) \" x=\"201.5\" xml:space=\"preserve\" y=\"198.25\">8<\/text> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"54.5\" xml:space=\"preserve\" y=\"140.25\">1<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"305.5\" xml:space=\"preserve\" y=\"140\">1<\/text> <g id=\"svg_18\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"286.5\" xml:space=\"preserve\" y=\"24.25\">+<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 304.50000000000006,18.249999999999975) \" x=\"299.5\" xml:space=\"preserve\" y=\"25.25\">8<\/text> <\/g> <g id=\"svg_21\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"151.5\" xml:space=\"preserve\" y=\"101.25\">+<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 169.5,95.24999999999999) \" x=\"164.5\" xml:space=\"preserve\" y=\"102.25\">8<\/text> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_22\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"66.5\" x2=\"150.5\" y1=\"135.25\" y2=\"101.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_23\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"214.5\" x2=\"298.5\" y1=\"177.25\" y2=\"143.25\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_24\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-21 147.50000000000006,102.25) \" x=\"141.5\" xml:space=\"preserve\" y=\"109.25\">><\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_25\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-20 295.50000000000017,144.25) \" x=\"289.5\" xml:space=\"preserve\" y=\"151.25\">><\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_26\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"178.5\" xml:space=\"preserve\" y=\"26.25\">2<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_27\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"109.5\" xml:space=\"preserve\" y=\"66\">+<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_28\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"238.5\" xml:space=\"preserve\" y=\"66\">+<\/text> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> 2","B.<\/strong> 3","C.<\/strong> 1","D.<\/strong> 0"],"correct":"3","level":"2","hint":"S\u1eed d\u1ee5ng b\u1ea3ng bi\u1ebfn thiên c\u1ee7a hàm phân th\u1ee9c.<\/p>","answer":"Ch\u1ecdn C.<\/strong> 1.<\/span><\/p>Hàm s\u1ed1 $f(x)=\\dfrac{ax+1}{bx+c}$<\/span> có \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng là \u0111\u01b0\u1eddng th\u1eb3ng $x=-\\dfrac{c}{b}$<\/span> và \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang là \u0111\u01b0\u1eddng th\u1eb3ng $y=\\dfrac{a}{b}$<\/span>.<\/p>T\u1eeb b\u1ea3ng bi\u1ebfn thiên ta có $-\\dfrac{c}{b}=2$<\/span> và $\\dfrac{a}{b}=1$<\/span> ⇔ $a=b=-\\dfrac{c}{2}$<\/span>    (1).<\/p>M\u1eb7t khác $f^\\prime(x)=\\dfrac{ac-b}{(bx+c)^2}$<\/span>.<\/p>Vì hàm s\u1ed1 \u0111ã cho \u0111\u1ed3ng bi\u1ebfn trên các kho\u1ea3ng $(-\\infty;2)$<\/span> và $(2;+\\infty)$<\/span> nên $f^\\prime(x)=\\dfrac{ac-b}{(bx+c)^2}>0$<\/span> ⇔ ac – c > 0    (2).<\/p>Thay (1) vào (2), ta \u0111\u01b0\u1ee3c  $-\\dfrac{c^2}{2}+\\dfrac{c}{2}>0$<\/span> ⇔ $-c^2+c>0$<\/span> ⇔ 0 < c < 1.<\/p>Suy ra c là s\u1ed1 d\u01b0\u01a1ng và a, b là s\u1ed1 âm.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-07-07 01:42:05","option_type":"txt","len":0},{"id":"5430","post_id":"7532","mon_id":"1159285","chapter_id":"1159288","question":"Cho hàm s\u1ed1 $f(x)=ax^3+bx^2+cx+d$<\/span>, v\u1edbi a, b, c, d ∈ R, có b\u1ea3ng bi\u1ebfn thiên nh\u01b0 sau. Có bao nhiêu s\u1ed1 d\u01b0\u01a1ng trong các s\u1ed1 a, b, c, d?<\/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_1\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"-1.5\" x2=\"320.5\" y1=\"29.25\" y2=\"29\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"-1.5\" x2=\"320.5\" y1=\"62.25\" y2=\"62\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"35.5\" x2=\"36\" y1=\"0.25\" y2=\"202.25\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-style=\"italic\" font-weight=\"bold\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"-0.5\" xml:space=\"preserve\" y=\"50.25\">f '(x)<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-style=\"italic\" font-weight=\"bold\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"11.5\" xml:space=\"preserve\" y=\"20.25\">x<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-style=\"italic\" font-weight=\"bold\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"4.5\" xml:space=\"preserve\" y=\"136.25\">f(x)<\/text> <g id=\"svg_10\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"37.5\" xml:space=\"preserve\" y=\"10.25\">_<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(90 53,14.250000000000005) \" x=\"48.5\" xml:space=\"preserve\" y=\"20.25\">8<\/text> <\/g> <g id=\"svg_13\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"38\" xml:space=\"preserve\" y=\"186.25\">_<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(90 53.49999999999998,190.25000000000003) \" x=\"49\" xml:space=\"preserve\" y=\"196.25\">8<\/text> <\/g> <g id=\"svg_16\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"296.5\" xml:space=\"preserve\" y=\"21.25\">+<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(90 311,15.00000000000003) \" x=\"306.5\" xml:space=\"preserve\" y=\"21\">8<\/text> <\/g> <g id=\"svg_19\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"297\" xml:space=\"preserve\" y=\"79.25\">+<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(90 311.50000000000006,73.00000000000003) \" x=\"307\" xml:space=\"preserve\" y=\"79\">8<\/text> <\/g> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-style=\"normal\" font-weight=\"bold\" id=\"svg_20\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"127.5\" xml:space=\"preserve\" y=\"20\">-2<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_21\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"217.5\" xml:space=\"preserve\" y=\"20\">0<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_22\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"133\" xml:space=\"preserve\" y=\"50\">0<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_23\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"217.5\" xml:space=\"preserve\" y=\"50.25\">0<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_24\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"132.5\" xml:space=\"preserve\" y=\"115.25\">2<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_25\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"218\" xml:space=\"preserve\" y=\"145.25\">1<\/text> <line fill=\"none\" id=\"svg_26\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"63.5\" x2=\"123.5\" y1=\"181.25\" y2=\"121.25\"><\/line> <line fill=\"none\" id=\"svg_27\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"148.5\" x2=\"211.5\" y1=\"112.25\" y2=\"138.25\"><\/line> <line fill=\"none\" id=\"svg_28\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"231.5\" x2=\"296.5\" y1=\"138.25\" y2=\"84.25\"><\/line> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_29\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-44 122.00000000000001,122.25000000000003) \" x=\"116.5\" xml:space=\"preserve\" y=\"128.25\">><\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_30\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(28 210.00000000000014,138.24999999999994) \" x=\"204.5\" xml:space=\"preserve\" y=\"144.25\">><\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_31\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-36 296.00000000000006,85.25000000000001) \" x=\"290.5\" xml:space=\"preserve\" y=\"91.25\">><\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_32\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"82.5\" xml:space=\"preserve\" y=\"50\">+<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" id=\"svg_33\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"258.5\" xml:space=\"preserve\" y=\"50\">+<\/text> <text fill=\"#000000\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"18\" font-weight=\"bold\" id=\"svg_34\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"175.5\" xml:space=\"preserve\" y=\"40.25\">_<\/text> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> 2","B.<\/strong> 3","C.<\/strong> 1","D.<\/strong> 4"],"correct":"2","level":"2","hint":"S\u1eed d\u1ee5ng b\u1ea3ng bi\u1ebfn thiên c\u1ee7a hàm s\u1ed1 b\u1eadc 3.<\/p>","answer":"Ch\u1ecdn B.<\/strong> 3.<\/span><\/p>T\u1eeb dáng \u0111i\u1ec7u s\u1ef1 bi\u1ebfn thiên hàm s\u1ed1 ta có a > 0. Khi x = 0 thì y = d = 1 > 0. M\u1eb7t khác $f^\\prime(x)=3ax^2+2bx+c$<\/span>. <\/p>T\u1eeb b\u1ea3ng bi\u1ebfn thiên ta có f'(x) = 0<\/strong> ⇔ x = –2 ho\u1eb7c x = 0.<\/p>T\u1eeb \u0111ó suy ra c = 0; $-\\dfrac{2b}{3a}=-2$<\/span> ⇔ b = 3a > 0.<\/p>V\u1eady có 3 s\u1ed1 d\u01b0\u01a1ng là a, b, d.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-07-07 01:58:40","option_type":"txt","len":0}]}