Question

How to find two numbers that sum equal 15 and product are maximized?

Answer 1

X - the first number15 - x - the second numberx(15 - x) - the product of the our numbers 
f(x) = -x^2 + 15x

The maximum value is in the vertex of parabola (h; k).
For ax² + bx + c:
$h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{b^2+4ac}{4a}$
We have: a = -1; b = 15; c = 0
substitute:
$h=\dfrac{-15}{2\cdot(-1)}=\dfrac{15}{2}=7.5$
15 - 7.5 = 7.5
Answer: 7.5 and 7.5.