Question

HELP!!!!!
Calculus reading problem:

the sum of two nonnegative numbers is 36. Find these numbers if the first plus the square of the second is a maximum..

Answer 1

-x -y = 36

x + (y)^(1/2) = f(x)

Answer 2

isolate one of the variables from the equation -x - y = 36 and sub it into the second equation then take the derivative and check where it is increasing and decreasing to get the max, then sub the max into the original equation to solve for the other variable

Answer 3

let x, y be the numbers...
x+y = 36, x>=0, y>=0.
f = x + y^(1/2)

use the first equation as a constraint to plug into the second equation. Maximize f by finding the derivative, f' and setting it to 0.

Answer 4

x+y^2 is a maximum
x=36-y
36-y+y^2 =f(x)
f'(x)=2y-1=0
y=1/2
(1/2)^2-1/2+36=35.75
The numbers are 1/2 and 35.75