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Giải bài 9.47 trang 66 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Viết phương trình tiếp tuyến của đồ thị hàm số \(y = {\left( {{x^2} - 1} \right)^2} - 3\) tại các giao điểm của nó với đồ thị hàm số \(y = 10 - {x^2}\).

𒐪Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Viết phương trình tiếp tuyến của đồ thị hàm số \(y = {\left( {{x^2} - 1} \right)^2} - 3\) tại các giao điểm của nó với đồ thị hàm số \(y = 10 - {x^2}\).

Phương pháp giải - Xem chi tiết

Tìm tọa độ giao điểm bằng cách giải phương trình \({\left( {{x^2} - 1} \right)^2} - 3 = 10 - {x^2}\). Giải phương trình ta được nghiệm \(x = 2\) và \(x =  - 2\).  Toạ độ các giao điểm là \(A\left( {2;6} \right)\) và \(B\left( { - 2;6} \right)\). Viết phương trình các tiếp tuyến tại \(A\left( {2;6} \right)\) và \(B\left( { - 2;6} \right)\).

Lời giải chi tiết

Phương trình hoành độ giao điểm: \({\left( {{x^2} - 1} \right)^2} - 3 = 10 - {x^2}\).Giải phương trình ta được nghiệm \(x = 2\) và \(x =  - 2\). Toạ độ các giao điểm là \(A\left( {2;6} \right)\) và \(B\left( { - 2;6} \right)\).Phương trình các tiếp tuyến cần tìm là \(y = 24x - 42\) và \(y =  - 24x - 42\)

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