Quick Answer: Can A Function Be Continuous And Not Differentiable?

How do you know if a function is 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..

At what point is a function not differentiable?

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.

Which of the following function is continuous everywhere but fails to be differentiable exactly two points?

Solution: An example of a function which is continuous everywhere but fails to be differentiable exactly at two points is x + |x – 1|. The functions is continuous everywhere but fails to be differentiable exactly at two points x = 0 and x = 1.

Which function are always continuous?

The most common and restrictive definition is that a function is continuous if it is continuous at all real numbers. In this case, the previous two examples are not continuous, but every polynomial function is continuous, as are the sine, cosine, and exponential functions.

How do you know if a function is continuous?

How to Determine Whether a Function Is Continuousf(c) must be defined. The function must exist at an x value (c), which means you can’t have a hole in the function (such as a 0 in the denominator).The limit of the function as x approaches the value c must exist. … The function’s value at c and the limit as x approaches c must be the same.

Why does a function have to be continuous to be differentiable?

Until then, intuitively, a function is continuous if its graph has no breaks, and differentiable if its graph has no corners and no breaks. So differentiability is stronger. A function is only differentiable on an open set, then it has no sense to say that your function is differentiable en a or on b.

Does there exist a function which is continuous everywhere but not differentiable?

Yes, there are some function which are continuous everywhere but not differentiable at exactly two points. … Since we know that modulus functions are continuous at every point, So there sum is also continuous at every point.

Why polynomial functions are continuous?

In other words all polynomials are differentiable for all (this is known as being everywhere differentiable) and any function that is differentiable at a point is continuous at that point. Thus all polynomials are everywhere continuous.

Why is a function continuous but not differentiable?

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.

Is a function continuous if it has a hole?

This kind of discontinuity is called a removable discontinuity. Removable discontinuities are those where there is a hole in the graph as there is in this case. … In other words, a function is continuous if its graph has no holes or breaks in it. For many functions it’s easy to determine where it won’t be continuous.

Are all continuous functions differentiable?

. 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.