10 câu hỏi liên quan đến khảo sát hàm số

10 câu hỏi liên quan đến khảo sát hàm số

Gửi bàigửi bởi thaothu vào ngày Thứ 6 16/03/12 17:00

Câu 1.
Viết phương trình tiếp tuyến của đồ thị hàm số biết tiếp tuyến cắt Ox, Oy lần lượt tại A,B mà tam giác OAB thỏa mãn AB = OA
Câu 2.
Tìm các giá trị của m để hàm số có cực đại , cực tiểu đồng thời là độ dài các cạnh góc vuông của một tam giác vuông có độ dài cạnh huyền bằng
Câu 3.
Tìm tất cả các giá trị m sao cho trên đồ thị (Cm): tồn tại đúng 2 điểm có hoành độ dương mà tiếp tuyến tại đó vuông góc với đường thẳng (L): x +2y - 3= 0
Câu 4.
Viết phương trình đương thẳng d cắt đồ thị (C): tại 3 điểm phân biệt A,B,C sao cho .
Câu 5.
Cho hàm số , với m là tham số. Tìm m để đường thẳng d: y = -x + 1 cắt đồ thị tại 3 điểm A(0;1), B,C và B,C đối xứng qua đường phân giác thứ nhất.
Câu 6.
Cho hàm số , m là tham số thực. Xác định m để hàm số đã cho có 3 cực trị tạo thành một tam giác có diện tích bằng 1.
Câu 7.
Cho hàm số . Viết phương trình tiếp tuyến của đồ thị biết tiếp tuyến cắt Ox,Oy tại A,B sao cho bán kính vòng tròn nội tiếp tam giác OAB lớn nhất.
Câu 8.
Cho hàm số . Gọi I là giao điểm 2 tiệm cận. Tìm m để tiếp tuyến bất kỳ của hàm số cắt hai tiệm cận tại A,B sao cho diện tích tam giác IAB bằng 64?
Câu 9.
Tìm m sao cho đồ thị hàm số cắt trục hoành tại 4 điểm phân biệt sao cho diện tích hình phẳng giới hạn bởi (C) và trục hoành có phần trên bằng phần dưới.
Câu 10.
Cho hàm số . Tìm m để hàm số đã cho có ba điểm cực trị và ba điểm cực trị này tạo thành một tam giác có diện tích lớn nhất.
thaothu
 
 
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Re: 10 câu hỏi liên quan đến khảo sát hàm số (tt)

Gửi bàigửi bởi thaothu vào ngày Thứ 6 16/03/12 17:22

Câu 11.
Cho hàm số có đồ thị (H). Tìm trên (H) điểm M để tiếp tuyến tại M có hệ số góc lớn hơn 1 tạo với đường thẳng : 3x +4y - 1 = 0 và một góc có giá trị cos là
Câu 12.
Cho hàm số có đồ thị (H). Tìm m để đường thẳng d: y = -x+m +1 cắt (H) tại hai điểm phân biệt A,B sao cho góc AOB nhọn.
Câu 13.
Cho hàm số . Viết phương trình tiếp tuyến của đồ thị (H) của hàm số đã cho biết tiếp tuyến tạo với hai đường tiệm cận một tam giác có chu vi bằng 2.(2+)
Câu 14.
Cho hàm số (1). Chứng minh với mọi giá trị thực khác 0 của m thì đồ thị hàm số (1) cắt d: y = 2x - 2m tại 2 điểm phân biệt A,B thuộc một đường (H)cố định. Đường thẳng d cắt các trụ Ox, Oy lần lượt tại các điểm M,N . Tìm m để diện tích tam giác AOB gấp ba lần diện tích tam giác OMN.
Câu 15.
Tìm trên (H): các điểm A,B sao cho độ dài đoạn thẳng AB bằng 4 và đường thẳng AB vuông góc với đường thẳng y = x
Câu 16.
Tìm m để đồ thị hàm số cắt trục hoành tại 4 điểm phân biệt có hoành độ lớn hơn -2
Câu 17.
Cho hàm số có đồ thị (H). Tìm m để đường thẳng d: y = 2x +3m cắt (H) tại hai điểm phân biệt sao cho với O là gốc tọa độ.
Câu 18.
Tìm tọa độ hai điểm B,C thuộc hai nhánh khác nhau của đồ thị sao cho tam giác ABC vuông cân tại A(2;1)
Câu 19.
Cho hàm số (1). Tìm m để hàm số (1) có 2 điểm cực trị A,B sao cho
Câu 20.
Cho hàm số có đồ thị (C). Tìm m để đường thẳng d: y = x+m cắt (C) tại 2 điểm phân biệt A,B sao cho AB = 2.
thaothu
 
 
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Re: 10 câu hỏi liên quan đến khảo sát hàm số (tt)

Gửi bàigửi bởi thaothu vào ngày Thứ 6 16/03/12 18:20

Câu 21.
Cho hàm số (C). Gọi I là giao điểm của 2 tiệm cận đồ thị.
Viết phương trình tiếp tuyến d của đồ thị biết d cắt tiệm cận đứng và tiệm cận ngang lần lượt tại A và B thỏa mãn
Câu 22.
Cho hàm số có đồ thị (Cm). Tìm tất cả các giá trị của tham số m để đồ thị (Cm) có ba điểm cực trị tạo thành một tam giác có đường tròn ngoại tiếp đi qua điểm D(0,6;1,8)
Câu 23.
Cho hàm số có đồ thị (C) và điểm A thuộc (C) với hoành độ bằng a.
Tìm các giá trị thực của a biết tiếp tuyến của (C) tại A cắt đồ thị (C) tại hai điểm phân biệt B,C khác A sao cho AC = 3AB (B nằm giữa A và C).
Câu 24.
Cho hàm số (m là tham số). Tìm m để hàm số có 3 điểm cực trị tạo thành một tam giác có trọng tâm là gốc tọa độ O?
Câu 25.
Cho hàm số có đồ thị (Cm). Tìm tất cả các giá trị m sao cho trên (Cm)có điểm mà tiếp tuyến tại đó vuông góc với đường thẳng d: y = x + 2011
Câu 26.
Cho hàm số (1). Tìm m để đồ thị hàm số (1) cắt Ox tại 3 điểm phân biệt có hoành độ dương.
Sửa lần cuối bởi thaothu vào ngày Thứ 7 17/03/12 0:16 với 1 lần sửa trong tổng số.
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Re: 10 câu hỏi liên quan đến khảo sát hàm số (tt))

Gửi bàigửi bởi thaothu vào ngày Thứ 6 16/03/12 22:31

Câu 27.
Tìm m để diện tích hình phẳng giới hạn bởi đồ thị: và truc hoành nằm phía trên trục hoành bằng phần nằm phía dưới trục hoành.
Câu 28.
Tìm trên đồ thị hàm số các điểm A,B sao cho tiếp tuyến của đồ thị tại A song song với tiếp tuyến tại điểm B và AB =
Câu 29.
Gọi D là đường thẳng đi qua A(1;0) và có hệ số góc k. Tìm để D cắt đồ thị hàm số tại 2 điểm phâ n biệt M,N thuộc 2 nhánh khác nhau của đồ thị và AM = 2AN
Câu 30.
Tìm m để đường thẳng qua cực đại, cực tiểu của đồ thị hàm số cắt đường tròn tâm I(1;1) bán kính bằng 1 tại A,B mà diện tích IAB lớn nhất.
Câu 31.
Cho hàm số có đồ thị (H). Viết phương trình tiếp tuyến tại M trên (H) sao cho tiếp tuyến tại M cắt hai trục tọa độ Ox, Oy tại hai điểm A,B đồng thời đường trung trực AB đi qua gốc tọa độ O.
Câu 32.
Cho hàm số (với m là tham số)
Tìm m để hàm số có cực đại và cực tiểu đối xứng qua đường thẳng d: 72x-12y-35=0
Câu 33.
Cho hàm số có đồ thị (C). Chứng minh rằng khi m thay đổi thì đường thẳng d: y = m(x+1) luôn cắt đồ thị (C) tại một điểm A cố định và tìm m để đường thẳng d cắt (C) tại ba điểm phân biệt A,B,C đồng thời B,C cùng với gốc tọa độ O tạo thành một tam giác có diện tích bằng 1.
Câu 34.
Tìm tất cả các giá trị của m để đồ thị hàm số: có hai điểm cực trị với hoành độ lớn hơn 1.
Câu 35.
Tìm hai điểm A,B thuộc đồ thị hàm số sao cho các tiếp tuyến tại A,B có cùng hệ số góc và đường thẳng đi qua A,B vuông góc với đường thẳng x+y+2011=0
Câu 36.
Giải sử đồ thị hàm số cắt trục hoành tại 3 điểm phân biệt
Chứng minh rằng:
Sửa lần cuối bởi thaothu vào ngày Thứ 6 16/03/12 23:49 với 1 lần sửa trong tổng số.
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Re: 10 câu hỏi liên quan đến khảo sát hàm số

Gửi bàigửi bởi thaothu vào ngày Thứ 6 16/03/12 23:36

Câu 37.
Chứng minh rằng với mọi m phương trình luôn có nghiệm duy nhất.\
Câu 38.
Gọi d là đường thẳng đi qua M(2;0) và có hệ số góc k. Tìm k để d cắt đồ thị (C): tại 4 điểm phân biệt.
Câu 39.
Tìm m để điểm A(3;5) nằm trên đường thẳng nối 2 điểm cực trị của đồ thị hàm số
Câu 40.
Viết phương trình tiếp tuyến của đồ thị hàm số biết tiếp tuyến tiếp xúc với đồ thị tại 2 điểm phân biệt.
Câu 41.
Cho hàm số (1) với m là tham số. Tìm m để đồ thị hàm số (1) cắt trục hoành tại ba điểm phân biệt có hoành độ thỏa:
Câu 42.
Với mỗi tham số thực m, gọi (Cm) là đồ thị của hàm số: (1).
Chứng minh rằng khi m thay đổi, đường thẳng (m): luôn cắt (Cm) tại điểm A có hoành độ không đổi. Tìm m để (m) còn cắt (Cm) tại điểm khác A và tiếp tuyến của (Cm) tại hai điểm đó song song với nhau.
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Re: 10 câu hỏi liên quan đến khảo sát hàm số

Gửi bàigửi bởi thaothu vào ngày Thứ 7 17/03/12 22:16

Câu 43.
Cho hàm số với m là tham số. Tìm m để tiếp tuyến có hệ số góc nhỏ nhất của đồ thị hàm số đã cho đi qua điểm A(1;)?
Câu 44.
Cho hàm số có đồ thị là (H). Tìm điểm M thuộc (H) sao cho tiếp tuyến tại M cắt 2 đường tiệm cận của (H) tại hai điểm A,B sao cho đường tròn ngoại tiếp tam giác IAB có bán kính nhỏ nhất với I là giao điểm của hai đường tiệm cận.
Câu 45.
Cho hàm số . Tìm m để hàm số cực tiểu mà không có cực đại?
Câu 46.
Tìm các giá trị của m để đường thẳng d: 2mx - 2y +m+1=0 cắt đồ thị hàm số tại 2 điểm phân biệt A,B sao cho biểu thức đạt giá trị nhỏ nhất?
Câu 47.
Cho hàm số . Tìm trên trục tung các điểm mà qua nó chỉ có một đường tiếp tuyến đến đồ thị hàm số trên?
Câu 48.
Cho hàm số (Cm)
a. Tìm điểm cố định của họ (Cm)
b. Từ các điểm cố định của họ đồ thị viết các đường thẳng đi qua chúng với hệ số góc tính diện tích hình phẳng giới hạn bởi các đường thẳng vừa lập và trục Ox?
Câu 49.
Cho hàm số với m là tham số có đồ thị (Cm). Tìm m để đồ thị (Cm) có hai điểm phân biệt đối xứng nhau qua gốc tọa độ?
Câu 50.
Cho hàm số (1). Tìm tất cả các điểm M thuộc trục tung sao cho từ đó có thể kẻ được ba tiếp tuyến đến đồ thị hàm số (1)?
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Re: 10 câu hỏi liên quan đến khảo sát hàm số

Gửi bàigửi bởi thaothu vào ngày Thứ 7 17/03/12 22:17

Đáp án 50 câu hỏi liên quan đến khảo sát hàm số.
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