What function is continuous but not differentiable?
In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass.
How do you know if a function is not differentiable?
A function is not differentiable at a if its graph has a vertical tangent line at a. The tangent line to the curve becomes steeper as x approaches a until it becomes a vertical line. Since the slope of a vertical line is undefined, the function is not differentiable in this case.
How do you know if a function is continuous or discontinuous?
A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function’s value. Point/removable discontinuity is when the two-sided limit exists, but isn’t equal to the function’s value.
Can a function be both differentiable and non differentiable?
Continuous. When a function is differentiable it is also continuous. But a function can be continuous but not differentiable.
What is the difference between continuous and differentiable?
The difference between the continuous and differentiable function is that the continuous function is a function, in which the curve obtained is a single unbroken curve. It means that the curve is not discontinuous. Whereas, the function is said to be differentiable if the function has a derivative.
How do you write a discontinuous function?
A discontinuous function is a function that has a discontinuity at one or more values mainly because of the denominator of a function is being zero at that points. For example, if the denominator is (x-1), the function will have a discontinuity at x=1.
Is differentiable the same as continuous?
Simply put, differentiable means the derivative exists at every point in its domain. Consequently, the only way for the derivative to exist is if the function also exists (i.e., is continuous) on its domain. Thus, a differentiable function is also a continuous function.
What are the examples of non differentiable functions?
Generally the most common forms of non-differentiable behavior involve a function going to infinity at x, or having a jump or cusp at x. There are however stranger things. The function sin(1/x), for example is singular at x = 0 even though it always lies between -1 and 1.
What functions are not continuous?
If a function is not continuous at a point in its domain, one says that it has a discontinuity there. The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function.
What are the examples of non-differentiable functions?
Is differentiable stronger than continuous?
Differentiability is a much stronger condition than continuity. All that needs to happen to make a continuous function not differentiable at a point is to make it pointy there, or oscillate in an uncontrolled fashion. For example: is continuous everywhere, but not differentiable at .
Is f (x) differentiable if the derivative is continuous?
I learnt that a function is called “differentiable ” if the derivative (if it exists) of the function is continuous. Suppose a function f: R → R is differentiable, i.e., f ′ ( x) is continuous. Does that imply that f ( x) is also continuous?
How do you know if a function is continuously differentiable?
The derivative must exist for all points in the domain, otherwise the function is not differentiable. This might happen when you have a hole in the graph: if there’s a hole, there’s no slope (there’s a drop off!). A continuously differentiable function is a function that has a continuous function for a derivative.
What is not differentiable at x = 0?
In the case of functions of one variable it is a function that does not have a finite derivative. For example, the function f ( x) = | x | is not differentiable at x = 0, though it is differentiable at that point from the left and from the right (i.e. it has finite left and right derivatives at that point).
What are differentiable and non-differentiable functions?
Differentiable functions are ones you can find a derivative (slope) for. If you can’t find a derivative, the function is non-differentiable.