For each of the following utility functions over X = R 2 +, plot three indifference curves by hand, shade in an upper contour set, and identify

For each of the following utility functions over X = R 2 +, plot three indifference curves by hand, shade in an upper contour set, and identify whether the preference relation represented by the utility function is convex and monotone.

1. U(x) = x12 + x22

2. U(x) = x1 + 3x2