Suppose Aaron's preferences over the commodities x1 and x2 can be represented by the utility function, U(x1, x2)=f(x1)+x2.

Suppose Aaron's preferences over the commodities x1 and x2 can be represented by the utility function, U(x1, x2)=f(x1)+x2. Which conditions ensure that the utility maximizing commodity bundle will have some of both x1 and x2 (i.e., be an interior solution)?

f'(x)>0 and f''(x)>0

f'(x)>0 and f''(x)<0

f'(x)>0 and f''(x)<0 and, at current income and prices, both x1 and x2 are positive.

f'(x)>0 and f''(x)>0 and at current income and prices, both x1 and x2 are positive.