Why Is the Weierstrass Function Not Differentiable?

The rough shape of the graph is determined by the n = 0 term in the series: cos(πx). ... 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 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.

What makes a continuous function 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.