What is the minimum value of z if z=x^2+2y^2+6x-4y+22?

We have a stationary point 



therefore there exist an extremum at  this point.

therefore the extremum indeed is the minimum. 



So, the minimum is equal to 11.

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.