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[114770]
07/11/2020 4:47:02 AM
Khảo sát hàm số
Cho em xin bài giải câu b với ạ
Link câu hỏi: https://www.askmath.vn/cau-hoi/co-bao-nhieu-so-nguyen-duong-de-ham-so-dong-bien-tren-khoang/5b7b79dd-c60d-4670-8ccc-89c37a93ad90
$\begin{gathered} ycbt \Leftrightarrow y' \geqslant 0,\forall x > 0 \hfill \\ \Leftrightarrow 3{x^2} + 2(1 - 2m)x + 2 - m \geqslant 0,\forall x > 0 \hfill \\ \Leftrightarrow 3{x^2} + 2x + 2 \geqslant m(4x + 1),\forall x > 0 \hfill \\ \Leftrightarrow g(x) = \frac{{3{x^2} + 2x + 2}}{{4x + 1}} \geqslant m,\forall x > 0 \hfill \\ \Leftrightarrow m \leqslant \mathop {\min }\limits_{(0; + \infty )} g(x) = g\left( {\frac{1}{2}} \right) = \frac{5}{4}. \hfill \\ \end{gathered} $