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March 31st, 2012, 06:23 PM   #1
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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.
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April 5th, 2012, 09:01 PM   #2
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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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