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).