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May 30th, 2014, 09:29 AM  #1 
Newbie Joined: May 2014 From: Texas Posts: 8 Thanks: 0  help with functions
Let C denote the graph of y=1/x, x > 0. (a) Express the distance between the point P(1,0) and a point Q on C as a function of the xcoordinate of Q. (b) What is the domain of the distance function obtained in part (a)? (c) Use the graph of the distance function obtained in part (a) to estimate the point Q on C that is closest to the point P. 
May 30th, 2014, 11:42 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,689 Thanks: 2669 Math Focus: Mainly analysis and algebra 
Your point $Q(x,y)$ is on the line $y = \frac{1}{x}$. In other words we can write that the point $Q$ is $(x,\frac{1}{x})$. Now you have to work out the distance $s(x)$ between $P$ and $Q$. Can you do that? 
May 30th, 2014, 06:46 PM  #3 
Newbie Joined: May 2014 From: Texas Posts: 8 Thanks: 0 
I'm assuming its the distance formula but I'm not sure

May 30th, 2014, 07:50 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,689 Thanks: 2669 Math Focus: Mainly analysis and algebra 
That's it exactly.

May 31st, 2014, 07:17 AM  #5 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry 
The distance between points $\displaystyle (a_1 , b_1 )$ and $\displaystyle (a_2 , b_2)$ is $\displaystyle \sqrt{(a_1  a_2)^2 + (b_1  b_2)^2 }$


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