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.
As a result, the graph of a differentiable function must have a (non-vertical) tangent line at each point in its domain, be relatively smooth, and cannot contain any breaks, bends, or cusps. More generally, if x0 is a point in the domain of a function f, then f is said to be differentiable at x0 if the derivative f â²(x0) exists. This means that the graph of f has a non-vertical tangent line at the point (x0, f(x0)).