Question

Among all positive numbers a, b whose sum is 6 find those for which the product of the two numbers and their difference is largest.

Answer 1

a + b = 6
a = 6 - b
let y = maximum

ab = y
(6-b)b = y
-b^2 + 6b = y

[d/dx] -b^2 + 6b = [d/dx]y

-2b + 6 = dy/dx

dy/dx = 0

-2b +6 = 0

-2(b -3) = 0

Therefore, b = 3

a + b = 6
a + 3 = 6
a = 3

Therefore, b = 3

Answer 2

Sorry but apparently this is not right because this is my online homework and its telling me its incorrect >_< help....