NLIN PROG Problem... 1 /5 100% + 1. For each of the following functions whether it is convex, concave (strictly or weakly) or neither f (x ) - 10x -x? (ii) f (x) - x*+6x2 + 12x (iii) f (x) - 2x3 - 3x2 (iv) f ( x , , x 2 ) - x , x 2 - x - x (v) f (x, , x, ) - 3x, + 2x, +4x2 + x5 - 2x, x2 (vi) f (x, , x2) - 1+2x2+3x,*2 2. (i) Show that the function f(x,, x, ) - x x , defined for x, > 0, x, > 0 is strictly concave. (ii) Show that the function /(x , x, ) - x/ x , defined for x, = 0, x, > 0 is concave. (iii) Show that the Cobb - Douglas production function f(x x, )- Axax , with 0 0. 3. For the Cobb - Douglas production function /(x x, ) - 1x x5 . with A > 0, a, B > 0defined on R , show that Euler's Theorem applies