As we saw in figure 3.5, one way to show convexity of indifference curves is to show for any two points (x1,y1) and (x2,y2) on an indifference curve that promises U=k, the utility is associated with the point {( x1+x2)/2} and {( y1+y2)/2} is at least as great as k. Use this approach to discuss the convexity of the indifference curves for the following three functions.