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

Please explaining words.

The coldest point will be at the minimum (the lowest point) of the surface defined by the function of x and y.  The gradient of this surface in the x-direction is zero there, as is the gradient in the y-direction. These conditions can be used to find the values of x and y, which, when plugged back into the expression fgor temperature will give you the minimum value.

If you look at the contour plot at 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 it is easy to make out the x and y values at the minimum. Plug these in to get the minimum temperature (-5).

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