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Giải bài 9.34 trang 64 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Tiếp tuyến của đồ thị hàm số \(y = \frac{2}{3}{x^3} - 4{x^2} + 5x + 3\) với hệ số góc nhỏ nhất có phương trình là

🧸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 \(y = \frac{2}{3}{x^3} - 4{x^2} + 5x + 3\) với hệ số góc nhỏ nhất có phương trình là

A. \(y = 3x - 25\).                      

B. \(y =  - 3x + 25\).                    

C. \(y =  - 3x + \frac{{25}}{3}\).      

D. \(y = 3x - \frac{{25}}{3}\).

Phương pháp giải - Xem chi tiết

Tính \(y'\)

Tìm giá trị nhỏ nhất của hệ số góc từ đó tìm tọa độ tiếp điểm Viết phương trình tiếp tuyến

Lời giải chi tiết

Hệ số góc tiếp tuyến của đồ thị hàm số có dạng \(k = y' = 2{x^2} - 8x + 5\).Khi đó ta có: \(k = 2({x^2} - 4x + 4) = 2{(x - 2)^2} - 3 \ge  - 3\)Dấu "=" đạt được, \({k_a} =  - 3\), khi \(x = 2\) và \(y = \frac{7}{3}\).Phương trình tiếp tuyến cần tìm là: \(y - \frac{7}{3} =  - 3(x - 2) \Leftrightarrow y =  - 3x + \frac{{25}}{3}\)

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

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