# Differentiable Function

Awesome Fractals by Silvia Cordedda -- For the ones not familiar with fractals, a fractal is an image built with math, a repetition of the same geometric module over and over, with different dimensions, according to a mathematical function.

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The Weierstrass function is a function that is continuous everywhere (there are no discontinuous jumps in value), but differentiable nowhere (it is smooth nowhere). If you zoom in far enough, most continuous functions will look smooth, or at least be...

In particular, any differentiable function must be continuous at every point in its domain.

Similar to Fourier series, Taylor series is an expansion of an infinitely differentiable function about a point. A variation of Taylor series, called as Maclaurin Series taken about the point x=0.

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Theory and Applications of Differentiable Functions of Several Variables by S. M. Nikolskii Download

A Continuous Differentiable Function, 2011, oil, graphite and mixed media on paper on panel, 40" x 40"