Smooth vs. Non-smooth Functions

Smooth functions have a unique defined first derivative (slope or gradient) at every point. Graphically, a smooth function of a single variable can be plotted as a single

Non-smooth function f (x) = max{x − 1, x/2}, a quadratic function

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SOLVED: Question 2. Point (Tu; Ho) In the lecture, I learned that

calculus - Why is a vector function not smooth if $r'=0

Nonsmooth function and its smooth Legendre conjugate.

Smooth muscle, anatomy, Smooth

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Full article: A Smooth Nonparametric, Multivariate, Mixed-Data

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What is a smooth function?

Smoothness - Wikipedia

What is a non-smooth function? - Quora

Global optimization of non-smooth function - Mathematics Stack