find minima and maxima points of a function


On Fri, 6 Feb 2009, Robert Marik wrote:

< Leo Butler <l.butler <at> ed.ac.uk> writes:
< 
< > 
< > 
< > < Another problem: try the function x^2*log(x)/2-x^2/4 
< > < the point x=0 is not a local maximum (does not belong to the domain of the
< > < function). The problem is that solve(x*log(x)=0,x) returns x=0 which does not
< > < belong to the domain. 
< > 
< > x*log(x) has a limit as x->0, (0), so it is conventional to extend
< > x*log(x) to include x=0 in its domain. I believe that maxima does this
< > implicitly.
< > 
< 
< I don't think so. Try solve(x/sin(x),x) 
< 
< wxmaxima (not the last version of Maxima, however) on our server returns x=0. 
 
That is clearly a bug. Here is what I get on maxima-5.16.3

(%i495) solve(x*csc(x),x);

`solve' is using arc-trig functions to get a solution.
Some solutions will be lost.
(%o495)                      [x = acsc(0), x = 0]

Maxima is factoring the expression and it is not checking if the
factorisation is valid where it finds the possible solutions. 

Leo

-- 
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.