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Giải bài tập 1.48 trang 49 SGK Toán 12 tập 1 - Cùng khám phá

Đồ thị của hàm số \(y = {x^3} - 3{x^2} + 2\) là đường cong trong hình nào dưới đây?
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Đề bài

Đồ thị của hàm số \(y = {x^3} - 3{x^2} + 2\) là đường cong trong hình nào dưới đây?

Phương pháp giải - Xem chi tiết

Đồ thị hàm số bậc 3 \(a{x^3} + b{x^2} + cx + d\) thường có những đặc điểm như sau: - Có 2 cực trị hoặc không có cực trị nào. - Luôn nhận điểm uốn làm tâm đối xứng. - Khi ac < 0 thì 2 điểm cực trị sẽ nằm 2 phía so với trục Oy. - Nếu hệ số a > 0, đồ thị đi từ phía dưới bên trái (hướng xuống) lên phía trên bên phải (hướng lên). - Nếu hệ số a < 0, đồ thị đi từ phía trên bên trái (hướng lên) xuống phía dưới bên phải (hướng xuống). - Đồ thị luôn cắt trục tung tại một điểm (khi x = 0, giá trị này là d).

Lời giải chi tiết

Loại A vì có đến 3 cực trị. Theo đề bài ta có a = 1 > 0 nên đồ thị sẽ đi từ phía dưới bên trái, suy ra loại C. Theo đề bài ta có d = 2 nên đồ thị sẽ cắt trục tung tại điểm (0;2), suy ra loại B. Đáp án đúng là D.

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