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March 31st, 2012, 06:23 PM  #1 
Member Joined: Mar 2012 Posts: 30 Thanks: 0  which conclusion(s) can be made if you know the following? J
which conclusion(s) can be made if you know the following? Justify your conclusion(s) a. f'(c)=0, f(c) exists, f'(c?x)<0 and f'(c+?x)>0 b. f(1) exists, f'(1)>0, and f''(1)<0 a. I put an inflection slope=0 function increases in one direction and decreases in the other. b. I put increasing with x but rate of increase is decreasing. 
April 5th, 2012, 09:01 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: which conclusion(s) can be made if you know the followin
a) We may conclude there is a local minimum at x = c, via the first derivative test. f(x) is decreasing to the left of c and increasing to the right and stationary at x = c, thus (c,f(c)) is a local minimum. b) Correct. 

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