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August 30th, 2013, 12:13 AM  #1 
Senior Member Joined: Oct 2012 Posts: 460 Thanks: 0  f(x)= log(sqrt(x)qwt(x1)), extrema
Dear All! Please, can we find maximum and minimum from: ? Many thanks! p.s. I got this pic on wa: http://www.wolframalpha.com/input/?i=gr ... 8x1%29%29 But , I got completely other graph in maxima! Please what is the problem? Many thanks! 
August 31st, 2013, 03:45 AM  #2  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: f(x)= log(sqrt(x)qwt(x1)), extrema Quote:
Carefully looking at this inequality we can see the domain is Let So we need to find u' , then substitute , then set f'(x) to zero. Okay , substitute now into f'(x) and set equal to zero , For this to be 0 the expression inside parenthesis must be 0 , there is no other way... let's do this , Well , this is clearly impossible. The numeators are the same but the denominators are NOT the same so the fractions can never be equal. Conclusion , the derivative is never zero or UNDEFINED for x > 1 so there can be no local max or min. Note* The domain of f'(x) is x > 1 , we lost the equals sign for the derivative but x = 1 is still valid for f(x).  

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extrema, logsqrtxqwtx1 
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