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The temperature of a point (x,y) in the plane is given by the expression x^2 + y^2 - 4x + 2y. What is the temperature of the coldest point in the plane?

 Oct 31, 2014

Best Answer 

 #1
avatar+27310 
+10

The following 3d plot and contour plot might help:

3d and contour plots

Note also that the gradient in the x-direction is 2x - 4 and in the y-direction is 2y + 2, and that these gradients must be zero at the minimum.

Find the values of x and y from 2x - 4 = 0 and 2y + 2 = 0, then put these values back into your expression for temperature.

 Nov 1, 2014
 #1
avatar+27310 
+10
Best Answer

The following 3d plot and contour plot might help:

3d and contour plots

Note also that the gradient in the x-direction is 2x - 4 and in the y-direction is 2y + 2, and that these gradients must be zero at the minimum.

Find the values of x and y from 2x - 4 = 0 and 2y + 2 = 0, then put these values back into your expression for temperature.

Alan Nov 1, 2014
 #2
avatar+94976 
+5

Alan, I also answered this question a little while ago.  My answer is a bit simpler.   

 

 

http://web2.0calc.com/questions/the-temperature-of-a-point-nbsp-nbsp-in-the-plane-is-given-by-the-expression-nbsp-what-is-the-temperature-of-the-coldest-point-in-the-pla_3

 

This questin must have been asked several times which is confusing.   

 Nov 3, 2014
 #3
avatar+27310 
0

Melody, your answer is certainly simpler!

.

 Nov 3, 2014
 #4
avatar+94976 
0

 

Yes - but yours is more impressive.  :)

 Nov 3, 2014

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