\(-\dfrac{f'\left(x\right)}{\left[f\left(x\right)\right]^2}=-3x^2\Rightarrow\dfrac{1}{f\left(x\right)}=\int-3x^2dx=-x^3+C\)
\(\Rightarrow f\left(x\right)=\dfrac{1}{-x^3+C}\)
\(f\left(2\right)=-\dfrac{1}{9}\Rightarrow-\dfrac{1}{9}=\dfrac{1}{C-8}\Rightarrow C=-1\)
\(\Rightarrow f\left(x\right)=-\dfrac{1}{x^3+1}\Rightarrow f\left(1\right)=-\dfrac{1}{2}\)



