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Giải bài 11 trang 12 sách bài tập toán 12 - Cánh diều

Cho hàm số \(y = f\left( x \right)\) có đạo hàm \(f'\left( x \right) = {x^2}{\left( {{x^2} - 1} \right)^2}\left( {x - 2} \right),\forall x \in \mathbb{R}\). Số điểm cực trị của hàm số đã cho là: A. 1. B. 2. C. 3. D. 4.

🔜Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Cánh diều

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

Cho hàm số \(y = f\left( x \right)\) có đạo hàm \(f'\left( x \right) = {x^2}{\left( {{x^2} - 1} \right)^2}\left( {x - 2} \right),\forall x \in \mathbb{R}\). Số điểm cực trị của hàm số đã cho là:

A. 1.                            B. 2.                            C. 3.                            D. 4.

Phương pháp giải - Xem chi tiết

Các bước để tìm điểm cực trị của hàm số \(f\left( x \right)\):

Bước 1.💛 Tìm tập xác định của hàm số \(f\left( x \right)\).

Bước 2.👍 Tính đạo hàm \(f'\left( x \right)\). Tìm các điểm \({x_i}\left( {i = 1,2,...,n} \right)\) mà tại đó hàm số có đạo hàm bằng 0 hoặc không tồn tại.

Bước 3.♕ Sắp xếp các điểm \({x_i}\) theo thứ tự tăng dần và lập bảng biến thiên.

Bước 4.🍃 Căn cứ vào bảng biến thiên, nêu kết luận về các điểm cực trị của hàm số.

Lời giải chi tiết

Hàm số có tập xác định là \(\mathbb{R}\). Ta có: \(y' = 0\) khi \(x = 0;x =  - 1;x = 1\) hoặc \(x = 2\). Bảng xét dấu đạo hàm của hàm số:

Dựa vào bảng xét dấu đạo hàm ta có: Hàm số đạt cực tiểu tại \(x = 2\). Vậy hàm số có 1 điểm cực trị. Chọn A.

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