perplexus.info :: Just Math : Coldest point in coordinate

Coldest point in coordinate (Posted on 2020-11-01)

In a plane, the point (x,y) has temperature x²+y²-6x+4y. Determine the coldest point of the plane and its temperature.

No Solution Yet Submitted by Danish Ahmed Khan

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Cold logic (spoiler)

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The temperature is (x^2-6x) + (y^2+4y). These can be minimized separately.

z = x^2-6x is a parabola in the x-z plane. It has roots of 0 and 6, and a minimum at x=3. 3^2 - 6*3 = -9

Similarly, y^2+4y has a minimum at y = -2. That minimum is -4.

So the total minimum is -13 at (3,-2).

Posted by Steve Herman on 2020-11-01 07:18:31

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