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.
The function f(x) = x2 + 2x + 3 is differentiable everywhere, with the derivative f â²(x) = 2x + 2. This function has a unique critical point â1, because it is the unique number x0 for which 2x0 + 2 = 0. This point is a global minimum of f. The corresponding critical value is f(â1) = 2.