**Answer:**

\begin{equation}

\begin{array}{l}

\begin{array}{l}

f(x)=2 x^{3}-2 x^{2}+4 x-1 \\

f^{\prime}(x)=6 x^{2}-4 x+4 \\

f^{\prime \prime}(x)=12 x-4

\end{array}\\

f \text { is concaveup when } f^{\prime \prime}(x)>0\\

\therefore 12 x-4>0\\

\begin{array}{r}

12 x>4 \\

x>\frac{1}{3}

\end{array}

\end{array}

\end{equation}

**Explanation:**

This question requires in-depth understanding of the concept of concavity. You need to have both a visual and conceptual understanding of what it means to say that a function is concave up in a given interval or concave down in a given interval. To answer this question, you need to be conversant with the logical procedure of determining the interval on which a function is concave up. This higher order reasoning process entails the following procedural steps: You must first determine $f^{\prime}(x)$, and then calculate $f^{\prime \prime}(x)$, and finally solve $f^{\prime \prime}(x)>0$.