Cho Hàm Số $f(x)$ Có Bảng Xét Dấu Của đạo Hàm Như Hình Vẽ. Hàm ...

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Câu hỏi

Cho hàm số $f(x)$ có bảng xét dấu của đạo hàm như hình vẽ. Hàm số $y=3f(x)-x^3+3x$ đồng biến trên khoảng nào dưới đây?

A.

$(1;+\propto).$

B.

$(-\propto;-1).$

C.

$(-1;0)$.

D.

$(0;2)$.

Đáp án và lời giải Đáp án:C Lời giải:\[y = 3f\left( {x + 2} \right) - {x^3} + 3x.\,y' =3.\left[{f'\left( {x + 2} \right) + \left( {1 - {x^2}} \right)} \right]\]Ta có:\[f'\left( {x + 2} \right) \ge0\Leftrightarrow \left[ \begin{array}{l} 1 \le x + 2 \le 3\\x + 2 \ge 4\end{array} \right. \Leftrightarrow \left[ \begin{array}{l} 1 \le x \le 1\\x \ge 2\end{array} \right.\]Ta có \[\left\{ \begin{array}{l} f'\left( {x + 2} \right) \ge 0,\forall x \in \left( { - 1;1} \right)\\ 1 - {x^2} > 0,\forall x \in \left( { - 1;1} \right) \end{array} \right. \Rightarrow y' > 0,\forall x \in \left( { - 1;1} \right)\]

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