(a) Consumer C has the following utility function over her investments x. Negative values of x imply that she is selling the investments, while positive values of x indicate that she is buying it. Here, and are constant parameters. J(x)=(2x+)35x+8x2+12ifififx001 (3 marks) Given the utility function is continuous throughout the entire domain, determine whether the function is differentiable throughout the entire domain. (b) Consumer D has the following utility function over goods x and y. f(x,y)=(xy)ex+y The domain is given as follows: {(x,y:(x+1)2+(y+1)21} i. (3 marks) Determine whether the utility function is concave or convex. ii. (4 marks) Find the maximum and minimum utility. (a) Consumer C has the following utility function over her investments x. Negative values of x imply that she is selling the investments, while positive values of x indicate that she is buying it. Here, and are constant parameters. J(x)=(2x+)35x+8x2+12ifififx001 (3 marks) Given the utility function is continuous throughout the entire domain, determine whether the function is differentiable throughout the entire domain. (b) Consumer D has the following utility function over goods x and y. f(x,y)=(xy)ex+y The domain is given as follows: {(x,y:(x+1)2+(y+1)21} i. (3 marks) Determine whether the utility function is concave or convex. ii. (4 marks) Find the maximum and minimum utility