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# Find two numbers whose difference is $100$ and whose product is a minimum.

## $(x, y)=(50,-50)$

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all right, we've got a question here where we need to find two numbers whose differences 100 product is a minimum in the way we would solve this, we would say, Well, why minus X must equal to 100. So we would say, Well, why? With 200 minus X, we know the product why the X p X is going to be equal to Y times X. You could write that as 100 minus x times X, and we would get 100 X minus X. All right. Now, if he's took the derivative of P of X said is equal to zero, we could find a critical point 100 minus two x. So we would say Well to eggs equal to 100 that actually equal to 50. I'm sorry. I just realized this should be a positive here. That would be a positive here. Then that would make that a positive that make that positive, and this would make this a negative. So therefore you're why would then be equal to 100 plus negative 50. Just 50? These will be your two values or when you could get 100 has the difference. 15 minus negative. 50 And also get a minimum. Um, product. All right. Well, I hope that clarifies the question. And thank you so much for watching.

The University of Texas at Arlington

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