First Derivative Test
المؤلف:
Abramowitz, M. and Stegun, I. A
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
21-9-2018
1890
First Derivative Test
Suppose 
is continuous at a stationary point 
.
1. If 
on an open interval extending left from 
and 
on an open interval extending right from 
, then 
has a local maximum (possibly a global maximum) at 
.
2. If 
on an open interval extending left from 
and 
on an open interval extending right from 
, then 
has a local minimum (possibly a global minimum) at 
.
3. If 
has the same sign on an open interval extending left from 
and on an open interval extending right from 
, then 
has an inflection point at 
.
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 14, 1972.
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