Đáp án: A
Giải thích các bước giải:
$\begin{array}{l}
f'\left( x \right) + 3x.f\left( x \right) = 0\\
\Rightarrow \frac{{f'\left( x \right)}}{{f\left( x \right)}} + 3x = 0\\
\Rightarrow \frac{{f'\left( x \right)}}{{f\left( x \right)}} = - 3x\\
\Rightarrow \int {\frac{{f'\left( x \right)}}{{f\left( x \right)}}dx} = \int { - 3xdx} \\
\Rightarrow \int {\frac{1}{{f\left( x \right)}}d\left( {f\left( x \right)} \right)} = - \frac{3}{2}{x^2} + C\\
\Rightarrow \ln f\left( x \right) = - \frac{3}{2}{x^2} + C\\
Do:f\left( 1 \right) = 1\\
\Rightarrow 0 = - \frac{3}{2} + C\\
\Rightarrow C = \frac{3}{2}\\
\Rightarrow \ln f\left( x \right) = - \frac{3}{2}{x^2} + \frac{3}{2}\\
\Rightarrow \ln f\left( { - 1} \right) = - \frac{3}{2} + \frac{3}{2} = 0\\
\Rightarrow f\left( { - 1} \right) = 1
\end{array}$
