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Old January 1st, 2009, 12:48 AM
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Quote:
Originally Posted by OnMyWayToBeAMathProffesor View Post
a-answer) i got x=1 for a maximum because the f'(x) goes from negative y values to 0 back to negative y values. is this correct?
no. let \varepsilon >0. suppose f(a) exists. (a,f(a)) is a maximum point (minimum point) if
1. f'(a)=0 or f'(a) does not exist
2. f'(a-\varepsilon)> 0 and f'(a+\varepsilon)< 0 (f'(a-\varepsilon)< 0 and f'(a+\varepsilon)> 0).

Quote:
Originally Posted by OnMyWayToBeAMathProffesor View Post
b-answer) point of inflections occurs when f''(x)=0 ... correct?
no.. POI occurs at a if f(a) exists and f''(a-\varepsilon)f''(a+\varepsilon)<0

it doesn't really mean that if f''(x)=0 (or dne), then it is already a POI.

Quote:
Originally Posted by OnMyWayToBeAMathProffesor View Post
c-answer) i could never figure out how to do that on MHF but i have seen other people do it. All my graphs don't seem to work, but from the chart i think there are 2 separate functions?

any help, especially with c would be greatly appreciated. Thanks.
depending on the graph that you will make, either it will consists of one part or two part since there is no condition on f(-1).. however, if it exists, then the graph must be of one part only; otherwise, the graph is of 2 parts..
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