calculus problem

[Unregistered]

hi im having trouble with a calculus problem, im hoping for someone to help me out a bit with it:
2 positive numbers have sum n. what is the smallest value possible for the sum of their squares.

i know x+y=n, x>0 y>0 and were trying to minimize f(x)=x^2+y^2.
After this I am lost, can someone help PLEASE!!

*BB*

[Unregistered]

For help on problems, I would suggest physicsforums.com. My teacher-coach turned me onto that web site a few years back.

[Unregistered]

To minimize f(x) You should first get it into the form of f(x). That is the expression you have written down as f(x) is not f(x) but rather f(x,y), a function of two variables. This is the point were you use your constrant, i.e. x+y=n. Solving your constrant for y your can then plug this into your expression and get f(x)=x^2 + (n-x)^2. Now you minimize this equation in the normal method (i.e. take a derivative and find were the slope is zero). You should find that x=n/2 at this point you should check to make sure it actually is a minimum. Since f''(x)=4 the function is concave up and all is good.

Of course don't forget that you havn't answered the actual question yet you just found the x value that produces the answer (n^2)/2.

hi im having trouble with a calculus problem, im hoping for someone to help me out a bit with it:
2 positive numbers have sum n. what is the smallest value possible for the sum of their squares.

i know x+y=n, x>0 y>0 and were trying to minimize f(x)=x^2+y^2.
After this I am lost, can someone help PLEASE!!

*BB*