1 The water-soluble vitamins (B vitamins and vitamin C) are absorbed easily along with the water in the small intestine, where they then travel through the body via the blood vessels. 2  Fat-soluble vitamins (vitamins A, D, and K) are absorbed just like the fat mentioned above.
A function f is said to be continuously differentiable if the derivative f'(x) exists and is itself a continuous function. Though the derivative of a differentiable function never has a jump discontinuity, it is possible for the derivative to have an essential discontinuity. For example, the function.
geometrically, the function #f# is differentiable at #a# if it has a non-vertical tangent at the corresponding point on the graph, that is, at #(a,f(a))#. That means that the limit. #lim_{x\to a} (f(x)-f(a))/(x-a)# exists (i.e, is a finite number, which is the slope of this tangent line). When this limit exist, it is called derivative of #f# at #a# and denoted #f'(a)# or #(df)/dx (a)#.