Consider the function
Find the number of points at which the function has an extremum(i.e points of local maxima/minima).
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Both Captain Black and Noncomalg are correct.
I used the 2nd derivative test incorrectly.
Last edited by TheEmptySet; October 30th 2009 at 09:50 AM.
Is x=2 the only extremum
Originally Posted by TheEmptySet
Now for any notice thatwhen that
So m is a saddle point for every and is either a max or a min. Would your argument not mean that does not have a minima but only a saddle point at ?
(you have misinterpreted the second derivative test for classification of extrema)
Originally Posted by pankaj Consider the function
Find the number of points at which the function has an extremum(i.e points of local maxima/minima). considering the fact that the graph of a polynomial at the roots with even (odd) multiplicity touches (crosses) the x-axis, and hoping that nothing weird happens in between, i believe that the
number of required points is:
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