continuous, analytic, differentiable What is the relationship between continuous and analytic and differentiable for complex function? Solution 1. if a function is differentiable in an interval then it is continuous in that interval ie differentiability => continuity but the converse need not be true 2 . If a function is differentiable in the given region then it is analytic in the region If a function fails to be differentiable at a particular point in the region then it is not analytic.