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Formula sheet for Prelim 2
Thursday March 29 in Uris Hall Aud.
f is increasing where f
′
(x) > 0, f is decreasing where f
′
(x) < 0
If f
′
(c) = 0 then c is a critical point. This is a necessary condition for a point
to be a local maximum [or mimimum], i.e., so that there are
a < c < b so that
f(c) is the largest [or smallest] value of f on [a,b].
FIRST DERIVATIVE TEST.
If f
′
(x) > 0 for a < x < c and f
′
(x) < 0 for c < x < b,
x is a local maximum.
If f
′
(x) < 0 for a < x < c and f
′
(x) > 0 for c < x < b,
x is a local minimum.
SECOND DERIVATIVE TEST.
If f
′
(c)=0 and f
′′
(c)<0 then
f is concave at c
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 DURRETT
 Calculus, Critical Point

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