Find two numbers differing by 46 whose product is as small as possible.

The numbers are 23 and -23.

Step-by-step explanation:

If the two numbers are x and y, we can say that the product is

We need to eliminate a variable. To do that we use the fact that the difference between the two numbers has to be 46.

So we can say and plug that into the equation for P

From the information given we want the product P to be minimized. For this we find the derivative

Next, we find the critical points, we set the above equation equal to zero and solve for x

Since x = 23 is the only critical number, we can conclude that there’s actually an absolute minimum at x = 23

Thus, and

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step-by-step explanation:

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