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I’ve never seen a graph of a function that is “everywhere differentiable but nowhere monotone”. Why? - Quora

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...

When a supersonic jet flies by, a sonic boom is produced. The booming sound is a shock wave. Shock waves occur in other situations as well, such as in plasma. Shock waves produce damage. Its mathematical modeling is a challenge. For example, how to use differentiable function theory of calculus to handle a phenomena that has discontinuity. Some brilliant ideas in the talk from Professor Yuxi Zheng. For More information please visit http://www.yu.edu

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

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

Dirichlet’s function is nowhere continuous and nowhere differentiable. It is also nowhere Riemann integrable since its upper integral and lower integral do not equal anywhere.

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In mathematics, the directional derivative of a multivariate differentiable function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. #Glogster #DirectionalDerivative

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Continuous Nowhere Differentiable Functions: The Monsters of Analysis (Hardcover)

Differentiability with Functions and Absolute Valu

Mean Value Theorem - An Investigation

This activity engages the students in studying several continuous, non-continuous, differentiable, and non-differentiable functions to decide what conditions must be met to guaranteed the conclusions of the mean value theorem.

Local Linearity-Zooming In to “See” Differentiability

Zooming in on two different functions show students the difference between function that a differentiable and those that are not. In part II students investigate a second function for differentiability.