Cho hàm số \(f(x)\) thỏa mãn \(f\left( 2 \right) =  - \frac{1}{5},f\left( x \right) = {x^3}{\left[ {f\left( x \right)} \right]^2}\) v�

* Hướng dẫn giải

Ta có \(f'\left( x \right) = {x^3}{\left[ {f\left( x \right)} \right]^2} \Rightarrow \frac{{f'\left( x \right)}}{{{f^2}\left( x \right)}} = {x^3} \Rightarrow \int\limits_1^2 {\frac{{f'\left( x \right)}}{{{f^2}\left( x \right)}}{\rm{d}}x = \int\limits_1^2 {{x^3}{\rm{d}}x} } \)

\( \Leftrightarrow \left. {\left( { - \frac{1}{{f\left( x \right)}}} \right)} \right|_1^2 = \frac{{15}}{4} \Leftrightarrow  - \frac{1}{{f\left( 2 \right)}} + \frac{1}{{f\left( 1 \right)}} = \frac{{15}}{4} \Leftrightarrow f\left( 1 \right) =  - \frac{4}{5}\)