Consider the following function:

f(x) 5x1 2x2 2 x2 3  3x3x4 4x2 4 2x4 5 x2 5

3x5x6 6x2 6 3x6x7 x2 7.

Show that f(x) is convex by expressing it as a sum of functions of one or two variables and then showing (see Appendix 2) that all these functions are convex.