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# The temperature of a point in the plane is given by the expression . What is the temperature of the coldest point in the pla

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The temperature of a point  in the plane is given by the expression . What is the temperature of the coldest point in the plane?

Oct 31, 2014

#1
+27310
+10

The following 3d plot and contour plot might help:

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
+27310
+10

The following 3d plot and contour plot might help:

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
+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
+27310
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.

Nov 3, 2014
#4
+94976
0

Yes - but yours is more impressive.  :)

Nov 3, 2014