Contents
What is non differentiable function?
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.
Why is the Weierstrass function not differentiable?
With b carefully chosen as in the theorem, the graph becomes so jagged that there is no reasonable choice for a tangent line at any point; that is, the function is nowhere differentiable.
Is the Weierstrass function integrable?
Weierstrass’ function is an example of a function that is continuous, but nowhere differentiable, and can be visualized as being “infinitely wrinkled”.
Is the Weierstrass function smooth?
The Weierstrass function is continuous everywhere. Therefore, it is a derivative: every continuous function is integrable, and is the derivative of its own integral from to . However, the antiderivative of the Weierstrass function is certainly not smooth: it is everywhere differentiable once but nowhere twice.
Which function Cannot be differentiated?
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’s an example of a non function?
The equations y=±√x and x2+y2=9 are examples of non-functions because there is at least one x-value with two or more y-values.
Is there a function without a derivative?
What function Cannot be differentiated?
What does it mean to be continuous but not differentiable?
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.
What functions can be differentiated?
A derivative is a function which measures the slope. It depends upon x in some way, and is found by differentiating a function of the form y = f (x). When x is substituted into the derivative, the result is the slope of the original function y = f (x).