What is an example of a function that is not differentiable?

What is an example of a function that is not differentiable?

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 points are non-differentiable?

A function is non-differentiable where it has a “cusp” or a “corner point”. This occurs at a if f'(x) is defined for all x near a (all x in an open interval containing a ) except at a , but limx→a−f'(x)≠limx→a+f'(x) . (Either because they exist but are unequal or because one or both fail to exist.)

What does a non-differentiable function mean?

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A function that does not have a differential. 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).

Why would a function not be 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.

What does a non differentiable function mean?

What is a differentiable function example?

A function is said to be differentiable if the derivative of the function exists at all points in its domain. Particularly, if a function f(x) is differentiable at x = a, then f′(a) exists in the domain. Let us look at some examples of polynomial and transcendental functions that are differentiable: f(x) = x4 – 3x + 5.

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What functions are 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.

Is not differentiable at?

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.

How do you know if a function is differentiable?

Everything else may be misleading. A function is differentiable at a point, x 0, if it can be approximated very close to x 0 by f ( x) = a 0 + a 1 ( x − x 0). That is, up close, the function looks like a straight line.

Why is the function k not differentiable at x = 0?

Function k below is not differentiable because the tangent at x = 0 is vertical and therefore its slope which the value of the derivative at x =0 is undefined. Contrapositive of the above theorem: If function f is not continuous at x = a, then it is not differentiable at x = a.

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When is a graph not differentiable at x = 0?

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.

What is an example of non differentiable behavior?

6.3 Examples of non Differentiable Behavior. A function which jumps is not differentiable at the jump nor is one which has a cusp, like |x| has at x = 0. 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.