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Giải bài tập 1.1 trang 8 SGK Toán 12 tập 1 - Cùng khám phá

Cho hàm số liên tục trên các khoảng \(( - \infty ;1)\),\((1; + \infty )\)và có bảng biến thiên như sau Xác định các khoảng đơn điệu và cực trị của hàm số đã cho
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Đề bài

 
 
Cho hàm số liên tục trên các khoảng \(( - \infty ;1)\),\((1; + \infty )\)và có bảng biến thiên như sau

Xác định các khoảng đơn điệu và cực trị của hàm số đã cho
 

Phương pháp giải - Xem chi tiết

- Để xác định khoảng đơn điệu của hàm số ta áp dụng định lý: Cho hàm số \(y = f(x)\) có đạo hàm trên khoảng\(y = f(x)\), (có thể a là\( - \infty \) , b là \( + \infty \)) Nếu \(f'(x) > 0\) với mọi \(x \in (a;b)\) thì hàm số đồng biến trên khoảng \((a;b)\) Nếu \(f'(x) < 0\) với mọi \(x \in (a;b)\) thì hàm số nghịch biến trên khoảng \((a;b)\) - Để xác định cực trị của hàm số đã cho ta áp dụng mối liên hệ giữa sự tồn tại giữa cực trị và dấu của đạo hàm ở hoạt động 4 (Trang 6): Nếu đạo hàm có cực trị thì dấu của đạo hàm bên trái và bên phải điểm cực trị sẽ khác nhau.
 

Lời giải chi tiết

Theo bảng biến thiên ta có: -  Hàm số \(y = f(x)\) đồng biến trên các khoảng là \(( - \infty ;1)\) , (2;3) , (3,4) , \((5; + \infty )\) -  Hàm số \(y = f(x)\) nghịch biến trên các khoảng là (1;2) , (4;5) -  Hàm số \(y = f(x)\) có các điểm cực trị là 2 và 5
 

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