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Giải bài 35 trang 71 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Tiếp tuyến của đồ thị hàm số \(y = 2{x^3} - 3{x^2} - 11x + 13\) tại điểm \(M\) có hệ số góc là 1. Tìm toạ độ điểm \(M\).

💞Tổng 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

Tiếp tuyến của đồ thị hàm số \(y = 2{x^3} - 3{x^2} - 11x + 13\) tại điểm \(M\) có hệ số góc là 1. Tìm toạ độ điểm \(M\).

Phương pháp giải - Xem chi tiết

Tiếp tuyến của đồ thị hàm số \(y = f\left( x \right)\) tại điểm \(M\left( {{x_0};{y_0}} \right)\) có hệ số góc là \(f'\left( {{x_0}} \right)\)

Lời giải chi tiết

\(y' = 6{x^2} - 6x - 11\)Tiếp tuyến của đồ thị hàm số \(y = 2{x^3} - 3{x^2} - 11x + 13\) tại điểm \(M\left( {{x_0};{y_0}} \right)\) có hệ số góc là\(6x_0^2 - 6{x_0} - 11 = 1 \Leftrightarrow 6x_0^2 - 6{x_0} - 12 = 0 \Leftrightarrow \left[ \begin{array}{l}{x_0} =  - 1\\{x_0} = 2\end{array} \right.\)Vậy \(M\left( { - 1;19} \right)\) hoặc \(M\left( {2; - 5} \right)\).

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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