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

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

This article originally appeared in:
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.

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Capsule Course Topic(s):
One-Variable Calculus | Theoretical Issues
Sequences and Series | Special Series: General