Find $f$.
\[
\begin{array}{l}
f^{\prime \prime \prime}(x)=\cos (x), \quad f(0)=7, \quad f^{\prime}(0)=6, \quad f^{\prime \prime}(0)=9 \\
f(x)=
\end{array}
\]

Step 1 ：\(\int f^{\prime \prime \prime}(x) dx = \int \cos(x) dx = \sin(x) + C_1\)

Step 2 ：\(f^{\prime \prime}(0) = \sin(0) + C_1 = 9 \implies C_1 = 9\)

Step 3 ：\(f^{\prime \prime}(x) = \sin(x) + 9\)

Step 4 ：\(\int f^{\prime \prime}(x) dx = \int (\sin(x) + 9) dx = -\cos(x) + 9x + C_2\)

Step 5 ：\(f^{\prime}(0) = -\cos(0) + 9*0 + C_2 = 6 \implies C_2 = 7\)

Step 6 ：\(f^{\prime}(x) = -\cos(x) + 9x + 7\)

Step 7 ：\(\int f^{\prime}(x) dx = \int (-\cos(x) + 9x + 7) dx = -\sin(x) + \frac{9}{2}x^2 + 7x + C_3\)

Step 8 ：\(f(0) = -\sin(0) + \frac{9}{2}*0^2 + 7*0 + C_3 = 7 \implies C_3 = 7\)

Step 9 ：\(\boxed{f(x) = -\sin(x) + \frac{9}{2}x^2 + 7x + 7}\)