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𒆙 SBT Toán 12 - giải SBT Toán 12 - Cánh diều

Giải bài 13 trang 12 sách bài tập toán 12 - Cánh diều

Hàm số $y = {x^3} - 3{x^2} - 9x - 3$ đạt cực tiểu tại điểm: A. ‒1. B. 3. C. 2. D. ‒30.

🍸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

Hàm số $y = {x^3} - 3{x^2} - 9x - 3$ đạt cực tiểu tại điểm:

A. ‒1. B. 3. C. 2. D. ‒30.

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.𒁏 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: $y' = 3{{\rm{x}}^2} - 6{\rm{x}} - 9$ $y' = 0$ khi $x = - 1$ hoặc ${\rm{x}} = 3$. Bảng biến thiên của hàm số:

Dựa vào bảng biến thiên ta có: Hàm số đạt cực tiểu tại điểm $x = 3$. Chọn B.

Chia sẻ

Bình luận

Bình chọn:

4.9 trên 7 phiếu

ꦗ Giải bài 14 trang 12 sách bài tập toán 12 - Cánh diều Cho hàm số $y = f\left( x \right)$ liên tục trên $\mathbb{R}$ và có đồ thị như Hình 5. Số điểm cực trị của hàm số đã cho là: A. 2. B. 4. C. 1. D. 3.
⭕ Giải bài 15 trang 13 sách bài tập toán 12 - Cánh diều Cho hàm số $y = f\left( x \right)$ liên tục trên $\mathbb{R}$ và có đồ thị như Hình 6. Giá trị cực tiểu của hàm số đã cho là: A. 2. B. 1. C. ‒1. D. 0.
🤪 Giải bài 16 trang 13 sách bài tập toán 12 - Cánh diều Cho hàm số $y = f\left( x \right)$ có đạo hàm trên $\mathbb{R}$ và đồ thị hàm số $y = f'\left( x \right)$ như Hình 7. Số điểm cực trị của hàm số $y = f\left( x \right)$ là: A. 4. B. 3. C. 2. D. 1.
𒀰 Giải bài 17 trang 13 sách bài tập toán 12 - Cánh diều
Trong mỗi ý a), b), c), d), chọn phương án đúng (Đ) hoặc sai (S). Cho hàm số (y = {x^3} - 3{rm{x}} + 2). a) (y' = 3{{rm{x}}^2} - 3). b) (y' = 0) khi (x = - 1,x = 1). c) (y' > 0) khi (x in left( { - 1;1} right)) và (y' < 0) khi (x in left( { - infty ; - 1} right) cup left( {1; + infty } right)). d) Giá trị cực đại của hàm số là ${{f}_{CĐ}}=0$.
⛄ Giải bài 18 trang 13 sách bài tập toán 12 - Cánh diều Trong mỗi ý a), b), c), d), chọn phương án đúng (Đ) hoặc sai (S). Cho hàm số $y = f\left( x \right)$ có đạo hàm trên $\mathbb{R}$ và đồ thị hàm số $y = f'\left( x \right)$ như Hình 8. a) $f'\left( x \right) = 0$ khi $x = 0,x = 1,x = 3$. b) Hàm số $y = f\left( x \right)$ đồng biến trên khoảng $\left( { - \infty ;0} \right)$. c) $f'\left( x \right) > 0$ khi $x \in \left( {0;3} \right)$. d) Hàm số $y = f\left( x \right)$ đồng biến trên khoảng $\left( {0;3} \right)$.

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