Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Inflection point 
Name: dalia zygas
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
The plot of function y=4x-x^4 appears to have two inflection points. yet d^2y/dx^2 = -12x^2 = 0 ;x=0 only solution, hence only one inflection point. Please explain discrepancy.


Replies:
The function graph has no inflection point, since the second derivative does not change sign at x = 0. This is a common error of analysis using derivatives --- zeros of the second derivative must be tested further before they can be classified as inflection points. It seems that you should check carefully what has been plotted --- if a grapher has been used --- find a better one.

tee


Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory