= Solution
{c}
The value $f(\mathbf a,\mathbf b,\mathbf c)$ is twice the <signed area> of the <triangle> traversed in that order; it is positive for counterclockwise <orientation>. Choose <points> on the <parabola>
$$
\boxed{\mathbf p_i=(i,i^2),\qquad 1\le i\le n.}
$$
For $i<j<k$, subtracting the first row in the <determinant> and factoring gives
$$
\begin{aligned}
f(\mathbf p_i,\mathbf p_j,\mathbf p_k)
&=(j-i)(k^2-i^2)-(k-i)(j^2-i^2)\\
&=(j-i)(k-i)(k-j)>0.
\end{aligned}
$$
Each of the three factors is positive, proving the required property for every <integer> $n\ge3$.
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