Question

Using Calculus, find two positive numbers with sum of 100 and product as large as possible. (Answer: both numbers are 50, what are the steps?)

Answer 1

using x and y as the variables a good idea? x + y = 100?

Answer 2

yes

Answer 3

looking for max(x*y), and an equation to represent that?

Answer 4

now make y the subject

Answer 5

y = 100 - x

Answer 6

and form an eqauation for the area in terms of x

Answer 7

area = x * (100 - x)

Answer 8

You have that x + y = 100, and you want to maximize K = x*y, then we have
K = (100-x)*x
differentiating and making the equal to 0:
100-2x = 0 ==> x = 50, now find y

Answer 9

right
now find the derivative da/dx

Answer 10

DA = 1*(100-x) + x(0 - 1)

Answer 11

A = 100x - x^2

dA/dx = 100 - 2x = 0
2x = 100
x = 50

and finally y = 100-50 == 50

Answer 12

so, where y = 50 is the global maximum of that graph, which means the maximum area possible

Answer 13

thanks for the help