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August 30th, 2013, 01:13 AM   #1
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f(x)= log(sqrt(x)-qwt(x-1)), 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 ... 8x-1%29%29

But , I got completely other graph in maxima!
Please what is the problem?
Many thanks!
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August 31st, 2013, 04:45 AM   #2
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Re: f(x)= log(sqrt(x)-qwt(x-1)), extrema

Quote:
Originally Posted by ungeheuer
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 ... 8x-1%29%29

But , I got completely other graph in maxima!
Please what is the problem?
Many thanks!
I'm going to assume natural logarithm base e because no index was given on log. The first thing to do is find the domain , the argument of the logarithm must be > 0 , this means



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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