# The $$n$$th Derivative Test and Taylor Polynomials Crossing Graphs

by David K. Ruch (Metropolitan State College of Denver)

College Mathematics Journal
September, 2002

Subject classification(s): Calculus
Applicable Course(s): 3.0 Calculus

The author describes $$n$$th derivative test, a generalization of 2nd derivative test, then applies it to give a quick proof of a condition for determining when the graph of a function and its Taylor polynomials intersect.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.