$$
\begin{gathered}
f^{\prime}(x)=\int f^{\prime \prime}(x) d x=\int(7 x-2) d x=\frac{7}{2} x^{2}-2 x+C_{1} \\
0=f^{\prime}(-2)=\frac{7}{2}(-2)^{2}-2(-2)+C_{1}=14+4+C_{1}=18+C_{1} \\
0=\left(8+C_{1}\right. \\
C_{1}=-18 \\
f^{\prime}(x)=\frac{7}{2} \lambda^{2}-2 x-18 \\
f(x)=\int f^{\prime}(x) d x=\int\left(\frac{7}{2} x^{2}-2 x-18\right) d x=\frac{7}{6} x^{3}-x^{2}-18 x+C_{2} \\
-2=f(-2)=\frac{7}{6}(-2)^{3}-(-2)^{2}-18(-2)+C_{2}=-\frac{28}{3}-4+36+C_{2}=\frac{68}{3}+C_{2} \\
-2=\frac{68}{3}+C_{2} \\
C_{2}=-\frac{74}{3}
\end{gathered}
$$
