Question 1
Let $f(x) = x^{3} - x^{2}$. For a given value of $c$, the graph of $f(x)$, together with the graph of the line $c + x$, split the plane up into regions. Suppose that $c$ is such that exactly two of these regions have finite area. Find the value of $c$ that minimizes the sum of the areas of these two regions.