What functions are not differentiable?
What functions are 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.
Why is Weierstrass function not differentiable?
The higher-order terms create the smaller oscillations. 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.
What is a differentiable function example?
For example, the function f(x) = x3 is differentiable and its derivative is f′(x) = 3×2.
What function has no derivative?
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.
What functions have no derivative?
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 is differentiable math?
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain.
What does differentiable mean in math?
A function is differentiable at a point when there’s a defined derivative at that point. This means that the slope of the tangent line of the points from the left is approaching the same value as the slope of the tangent of the points from the right.
Can a non differentiable function be continuous?
This theorem is often written as its contrapositive: If is not continuous at , then is not differentiable at . Thus from the theorem above, we see that all differentiable functions on are continuous on . Nevertheless there are continuous functions on that are not differentiable on .
Where if anywhere is the function not differentiable?
We can say that f is not differentiable for any value of x where a tangent cannot ‘exist’ or the tangent exists but is vertical (vertical line has undefined slope, hence undefined derivative). Below are graphs of functions that are not differentiable at x = 0 for various reasons.
