What is the smallest value of $x^2+y^2$ when $x+y=6$? If $ x+y=6 $ then what is the smallest possible value for $x^2+y^2$?
Please show me the working to show where I am going wrong!
Cheers

Most reasonable and concrete solution is to find minima using derivatives.
As shown by DeltaLima. 
There are many ways to find the minima graphically: 
$x^2+y^2$ expression can be written as $x^2+y^2=K$(equation)(it represents parabola) and $x+y=6$ represents, a straight line. They will intersect for minimum and maximum value of $(x,y)$.
