ECON 2016: Calculus Concavity, Homogeneity, Local/Global Max/Min, Constrained Optimization and Nonlinear Programming 1. For each of the following functions whether it is convex, concave (strictly or weakly) or neither. (i) f(x) = 10x-x (ii) f(x) = x +6x +12x (iii) f (x) = 2x3 - 3x2 (iv) f ( x, , x2 ) = xX2 - x - x f (x,,*2) = 3x, + 2x/ +4x2 + 13 -2xX2 (vi) f(x,, x2 ) = x7+ 2x7+3x,*2 2. (i) Show that the function f(x, , x, ) = xxxy , defined for x, > 0, x, > 0 is strictly concave. (ii) Show that the function f(x,,x, )= xxxx . defined for x > 0, x, >0 is concave. (iii) Show that the Cobb - Douglas production function f(x,x, )= Ax" x, , with 0 0, x, > 0