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You are not logged in. #1 20060118 12:42:19
Extrema
#2 20060118 12:53:48
Re: ExtremaI can't be sure as you don't remember the function, but it is possibly because you didn't find the second derivative of the function. You see, the first derivative can equal zero indicating a local extrema. However, if the second derivative also equals zero at this point it is undefined. The case may be that the function did not have a real value at zero. This is what some call a discontinuity. There may even be a limit as the function approaches zero, but still have no value at that point. Again, the second derivative test would allow you to make this distinction. #3 20060118 13:07:18
Re: Extrema
It would be a saddle point. The slope of the graph is 0 at that point, but it is not a local max or min. For example, x^3 has a saddle point at (0,0). "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 