A function can still be continuous and not be differentable at a point. For
example, the absolute value function |*x*| is continuous at *x* = 0, but
the deriviatve is not defined at that point. Here we give an example of a
function, the Weierstrass function W, which is continuous everywhere but differentiable nowhere.

The Weierstrass function W defined as by

where 0 < *H* < 1 and *ω* > 1 is continuous and nondifferentiable
for all values of *x*. This function is well defined, for example, to 100
digits, we may calculate

However, Figure 1 shows a zoom on the Weierstrass function W_{0.3, 1.3}(*x*)
starting from the interval [0, 1] and slowly zooming by over six orders of magnitude.
The red point is (0.5, W_{0.3, 1.3}(0.5)).

Figure 1. A zoom on the point (0.5, W_{0.3, 1.3}(0.5)).

Compare the zoom on the Weierstrass function with the zoom demonstrated
on the differentiable functions page.