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[164545]
29/12/2022 1:22:47 AM
giúp em câu này với ạ
$\begin{gathered} y = {x^3} + 2\left( {{m^2} + 1} \right)x + 3 + m \Rightarrow y' = 3{x^2} + 2\left( {{m^2} + 1} \right) > 0,\forall x \in \left[ {0;1} \right] \hfill \\ \Rightarrow \mathop {\max }\limits_{\left[ {0;1} \right]} y = y\left( 1 \right) = 1 + 2\left( {{m^2} + 1} \right) + 3 + m;\mathop {\min }\limits_{\left[ {0;1} \right]} y = y\left( 0 \right) = 3 + m \hfill \\ \Rightarrow \mathop {\max }\limits_{\left[ {0;1} \right]} y - 3\mathop {\min }\limits_{\left[ {0;1} \right]} y = 1 \Leftrightarrow 1 + 2\left( {{m^2} + 1} \right) + 3 + m - 3\left( {3 + m} \right) = 1 \Leftrightarrow m = - 1;m = 2 \hfill \\ \end{gathered} $