MathDB

2010 Calculus #6: Splitting the Plane

Source:

July 15, 2012

calculusgeometry

Problem Statement

Let

f(x)=x^3-x^2

. For a given value of

x

, 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.