Answer
$$
f(x) =2 x^{2}-\frac{9}{28} x^{7 / 3}+C x+D
$$
where $C,D$ are arbitrary constants .
Work Step by Step
$$
f^{\prime \prime}(x)=4-\sqrt[3] {x}
$$
The general anti-derivative of $
f^{\prime \prime}(x)=4-\sqrt[3] {x} $ is
$$
f^{\prime}(x) =4x-\frac{3}{4} x^{\frac{4}{3}}+C
$$
Using the anti-differentiation rules once more, we find that
$$
\begin{split}
f(x) &=4 \cdot \frac{1}{2} x^{2}-\frac{3}{4} \cdot \frac{3}{7} x^{7 / 3}+C x+D \\
&=2 x^{2}-\frac{9}{28} x^{7 / 3}+C x+D
\end{split}
$$
where $C,D$ are arbitrary constants .