Well functioning society: trong Tiếng Việt, bản dịch, nghĩa, từ đồng nghĩa, nghe, viết, phản nghiả, ví dụ sử dụng
Functions
- « Previous
- Next »
Functions are one of the fundamental building blocks in JavaScript. A function in JavaScript is similar to a procedure—a set of statements that performs a task or calculates a value, but for a procedure to qualify as a function, it should take some input and return an output where there is some obvious relationship between the input and the output. To use a function, you must define it somewhere in the scope from which you wish to call it.
See also the exhaustive reference chapter about JavaScript functions to get to know the details.
Differentiability of real functions of one variableEdit
A function f:U→R{\displaystyle f:U\to \mathbb {R} }, defined on an open set U⊂R{\displaystyle U\subset \mathbb {R} }, is differentiable at a∈U{\displaystyle a\in U} if the derivative
exists. This implies that the function is continuous at a.
This function f is differentiable on U if it is differentiable at every point of U. In this case, the derivative of f is thus a function from U into R.{\displaystyle \mathbb {R} .}
A differentiable function is necessarily continuous [at every point where it is differentiable]. It is continuously differentiable if its derivative is also a continuous function.
Differentiability and continuityEdit
The absolute value function is continuous [i.e. it has no gaps]. It is differentiable everywhere except at the point x = 0, where it makes a sharp turn as it crosses the y-axis.
A cusp on the graph of a continuous function. At zero, the function is continuous but not differentiable.
If f is differentiable at a point x0, then f must also be continuous at x0. In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable. For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.
Most functions that occur in practice have derivatives at all points or at almost every point. However, a result of Stefan Banach states that the set of functions that have a derivative at some point is a meagre set in the space of all continuous functions.[1] Informally, this means that differentiable functions are very atypical among continuous functions. The first known example of a function that is continuous everywhere but differentiable nowhere is the Weierstrass function.