My Math Forum Minimum value?

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 February 9th, 2010, 10:06 AM #1 Newbie   Joined: May 2008 Posts: 11 Thanks: 0 Minimum value? Hey, how would I algebraically find the minimum value of...say... $y=sqrt(x^2+(x-1)^2)$?
 February 9th, 2010, 01:10 PM #2 Newbie   Joined: Dec 2009 Posts: 7 Thanks: 0 Re: Minimum value? If you differentiate your function, you will get: y´= 1/2 * (x2 +(x-1)2)**(-1/2) * (2x+2(x-1)), you can consider this as a product of two terms, the first one is always positive, a you are adding two positive numbers, so no minimum will came from here. the second terms has a possible solution: 4x-2=0 ==> x = 1/2
 February 9th, 2010, 03:33 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,747 Thanks: 2133 y² = x² + (x - 1)² = 2(x - 1/2)² + 1/2, so the minimum value of y is ?(1/2).

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