Find two positive numbers that satisfy the given requirements. the sum of the first number squared and the second number is 57 and the product is a maximum.

We're looking for two positive numbers that satisfy this constraint:

The question is, how would we find the maximum? Well, we can solve for y to get:

Now, we sub our new found y value into the product to get:

So, to find the extrema of this we have to figure out when the derivative is 0, so:

That would mean our second number would be 38, and the maximum product would be

english maybe i can ..