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Giải bài 9.45 trang 66 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho \(f\left( x \right) = {x^3} + a{x^2} + 3x + 1\) (\(a \in \mathbb{R}\) là tham số)

✱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

Cho \(f\left( x \right) = {x^3} + a{x^2} + 3x + 1\) (\(a \in \mathbb{R}\) là tham số) . Tìm \(a\) để \(f'\left( x \right) > 0\) với mọi \(x \in \mathbb{R}\).

Phương pháp giải - Xem chi tiết

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Lời giải chi tiết

Ta có \(f'\left( x \right) = 3{x^2} + 2ax + 3\). Do đó, \(f'\left( x \right) > 0\) với mọi \(x \in \mathbb{R}\) khi và chỉ khi\(3{x^2} + 2ax + 3 > 0,\forall x \Leftrightarrow \Delta ' = {a^2} - 9 < 0 \Leftrightarrow  - 3 < a < 3\).

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

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