October 28th, 2007, 06:51 PM  #1 
Member Joined: Sep 2007 Posts: 49 Thanks: 0  extreme values
Find the extreme values for this function: y=2x^28x+9. I got 2, so that y=1, but the books says '1' is the absolute minimum, but I think it should be local minimum because it didn't tell us the domain. Hope you can help, thanks.

October 28th, 2007, 09:23 PM  #2 
Newbie Joined: Oct 2007 From: Los Angeles Posts: 7 Thanks: 0 
the reason why it's an absolute minimum is because this is a parabola with a positive coefficient of the x^2 term. the point (2,1) is the vertex of the parabola.

October 28th, 2007, 11:09 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,480 Thanks: 2039 
If the domain is a real interval (such as all reals) that includes x = 2, the point (2, 1) is a local minimum and the absolute minimum.

October 29th, 2007, 03:21 PM  #4  
Member Joined: Sep 2007 Posts: 49 Thanks: 0  Quote:
 
October 29th, 2007, 05:15 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,480 Thanks: 2039 
y = 2(x − 2)² + 1


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