Key to Practice Midterm I

Problem 1

Problem 2

{(x,y)| x not +- y}

Problem 3

A.  Parabaloid

B.  Plain

C.  Cone

Problem 4

As a point moves away from the axes  in quadrant 1the point rises exponentially above the paper.  On the axes, the point is one unit above the paper.  As it moves from quadrant 1 to 2 the point dips to only one unit above the paper, slowly descending towards the paper as one moves farther into quadrant 2, then as one moves into quadrant 3, the point rises quickly again, back to 1 unit above on the negative y-axis and then descends towards the paper as it gets deeper into quadrant four.  

Problem 5

(0,0) is a Saddle Point, and (1,1) is a minimum.

Problem 6

3sqrt(6)