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Giải bài 1 trang 23 sách bài tập toán 12 - Chân trời sáng tạo

Chọn đáp án đúng. Biết rằng \(f'\left( x \right) = 8{{\rm{x}}^3} - 4x + 2\) và \(f\left( 1 \right) = 4\). Hàm số \(f\left( x \right)\) là A. \(2{x^4} - 2{x^2} + x + 4\). B. \(2{x^4} - 2{x^2} + 2x + 2\). C. \(8{x^4} - 4{x^2} + x\). D. \(8{x^4} - 4{x^2} + x + 4\).

💟Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Chân trời sáng tạo

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

Chọn đáp án đúng.

Biết rằng \(f'\left( x \right) = 8{{\rm{x}}^3} - 4x + 2\) và \(f\left( 1 \right) = 4\). Hàm số \(f\left( x \right)\) là

A. \(2{x^4} - 2{x^2} + x + 4\).

B. \(2{x^4} - 2{x^2} + 2x + 2\).

C. \(8{x^4} - 4{x^2} + x\).

D. \(8{x^4} - 4{x^2} + x + 4\).

Phương pháp giải - Xem chi tiết

‒ Sử dụng công thức \(\int {f'\left( x \right)dx}  = f\left( x \right) + C\). ‒ Sử dụng công thức: \(\int {{x^\alpha }dx}  = \frac{{{x^{\alpha  + 1}}}}{{\alpha  + 1}} + C\).

Lời giải chi tiết

\(f\left( x \right) = \int {f'\left( x \right)dx}  = \int {\left( {8{{\rm{x}}^3} - 4x + 2} \right)dx}  = 2{{\rm{x}}^4} - 2{{\rm{x}}^2} + 2{\rm{x}} + C\) \(f\left( 1 \right) = 4 \Leftrightarrow {2.1^4} - {2.1^2} + 2.1 + C = 4 \Leftrightarrow C = 2\) Vậy \(f\left( x \right) = 2{{\rm{x}}^4} - 2{{\rm{x}}^2} + 2{\rm{x}} + 2\). Chọn B. 

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