Find two numbers whose difference is 96 and whose product is a minimum?

Question

How do I solve a problem like this?

Answer 1

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The product is x * (x - 96) = x^2 - 96x

Taking the derivative, we get 2x - 96. Any local minimum or maximum will be found where the derivative equals zero, so 2x - 96 = 0 and x = 48.

The numbers are -48 and 48, and their product is -2304.

Answer 2

I don't know any other way to solve it but to think about it a bit... and - assuming integers - I come up with -95 and 1. At first I was thinking 0 and 96, but then I saw it. It's -95 and 1.

Source(s): I know math, but had to solve this one by intuition