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

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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