# Calculus

In the space below, provide the larger of the positive integers that add to 10 and have the largest possible product

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1. larger number x
smaller number 10-x
product = xy = x(10-x)

(I predict using common sense that the two numbers will be 5 and 5)

P = 10x - x^2
this is a downwards parabola, and it will have a max at its vertex
the x of the vertex is -b/(2a) = -10/-2 = 5 , (see, I told you)
so the two numbers with the largest product (25) and a sum of 10 are 5 and 5

Since neither number is larger than the other, the phrasing of the question is bogus.

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