Speaker
Dr. Robert Kantrowitz, Hamilton College
Title
What does the condition f''' >= 0 tell us about f?
Physical Location
Allen Hall 411
Abstract: While basic calculus informs us how the first and second derivatives of a function provide insight into the shape of its graph, it is less apparent what geometric information is captured by higher derivatives. This talk is about functions whose third derivatives do not change sign on an interval. It turns out that each such function always enjoys a predictable relationship with two canonical quadratic polynomials that are associated with it. We shall also indicate the history of this problem and an application to the motion of a projectile in the plane.