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

Reed Danzinger - A Continuously Differentiable Function, 2011 oil, graphite, and mixed media on paper on panel 40 x 40 in

The Taylor Series of a real or complex-valued function f(x) that is infinitely differentiable at a real or complex number a is the power series; this serves as a way to approximate a polynomial

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

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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Exponential Functions

Zombies, cockroaches and bacteria! What more do you need :) If you want a project or activity that is differentiable, then you have found it. This activity gives the student choices, an avenue to be creative, a chance to learn cross-curricular content and of course an opportunity to learn about exponential functions!

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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