Is Continuous but Not Differentiable?

David Miller
David Miller
• • 6 min read

Differentiability and Continuity the Absolute Value Function Is Continuous (I. E. It Has No Gaps). It Is Differentiable Everywhere Except at the Point X = 0...

Is Continuous but Not Differentiable?

Differentiability and continuity
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 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.

Must Read

Is continuous function differentiable?

We see that if a function is differentiable at a point, then it must be continuous at that point. There are connections between continuity and differentiability. Differentiability Implies Continuity If is a differentiable function at , then is continuous at . ... If is not continuous at , then is not differentiable at .

David Miller

David Miller

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David Miller brings 15 years of experience in global economics, personal finance strategy, and market dynamics. He specializes in turning complex economic trends into actionable insights for everyday readers.