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=(-b)/(2a);\ k=f(h)=(b^2+4ac)/(4a)`
We have: a = -1; b = 15; c = 0
substitute:

`h=(-15)/(2\cdot(-1))=(15)/(2)=7.5`
15 - 7.5 = 7.5
Answer: 7.5 and 7.5.