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07122014, 07:04 PM  #1 (permalink) 
Seasoned Member Join Date: Dec 2008  who has some calculus chops?
There are some smart cookies on this board, so here goes! I need to find the relative extrema using the second derivative test if applicable. I have solved to the second derivative. I'm trying to find the possible inflection points. Setting it equal to zero gives X = sqrt1, so that doesn't exist since we aren't dealing with imaginary numbers. Leaving me to think, no inflection points. Next I tried setting the 1st derivative equal to 0 to find the critical numbers. Here is where I am truly confused. I think X = +/ 1 are the critical numbers. The book's solution in the back says only x=1 is a critical number. Why? Also, I have already tried Wolfram Alpha, it was no help. According the book, all of math up to the critical number is correct. They don't show how to solve for the critical number.
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07122014, 07:35 PM  #2 (permalink) 
Post Whore Join Date: Oct 2009 
I dont remember, but it might have to do with positive squares. This may be relevant. Square Root = Always Positive? : GMAT Quantitative Section 
07172014, 10:40 AM  #4 (permalink) 
Bigger Balls Join Date: Sep 2006 Location: Leominster, MA 
Complex logarithms will come about, and they are easy to deal with. e.g. ln(1)=i*pi which is just another way of writing Euler's identity. You can use this to compute any complex log; i.e. ln(15) = ln(15) + i*pi Plugging that back in leaves you with +1/2 as a real result of the equation, with the imaginary component of pi; +1/2 is the same real result as x=+1, but there you only have the real solution. Last edited by Siress; 07172014 at 10:43 AM. 
07192014, 10:54 PM  #5 (permalink)  
Seasoned Member Join Date: Dec 2008  Quote:
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