SOLUTION: This is a calculus problem. Consider two integers x and y such that x−y=12. What value of y will minimize x^2+y^2?

Algebra ->  Trigonometry-basics -> SOLUTION: This is a calculus problem. Consider two integers x and y such that x−y=12. What value of y will minimize x^2+y^2?       Log On


   

Question 858571: This is a calculus problem. Consider two integers x and y such that x−y=12. What value of y will minimize x^2+y^2?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
L=x%5E2%2By%5E2
Substitute,
x-y=12
x=12%2By
.
.
L=%2812%2By%29%5E2%2By%5E2
L=%28144%2B24y%2By%5E2%29%2By%5E2
L=2y%5E2%2B24y%2B144
Take the derivative of L with respect to y and set it to zero.
dL%2Fdy=4y%2B24=0
4y%2B24=0
4y=-24
y=-6
Then,
x=12-6
x=6