Inflection Point
المؤلف:
Bronshtein, I. N.; Semendyayev, K. A.; Musiol, G.; and Muehlig, H
المصدر:
Handbook of Mathematics, 4th ed. New York: Springer-Verlag, 2004
الجزء والصفحة:
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21-9-2018
2651
Inflection Point
An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima. For example, for the curve 
plotted above, the point 
is an inflection point.
The first derivative test can sometimes distinguish inflection points from extrema for differentiable functions 
.
The second derivative test is also useful. A necessary condition for 
to be an inflection point is 
. A sufficient condition requires 
and 
to have opposite signs in the neighborhood of 
(Bronshtein and Semendyayev 2004, p. 231).
REFERENCES:
Bronshtein, I. N.; Semendyayev, K. A.; Musiol, G.; and Muehlig, H. Handbook of Mathematics, 4th ed. New York: Springer-Verlag, 2004.
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