Questions tagged [piecewise-continuity]

For use when asking questions about piecewise continuous functions, their properties, or the functional branch itself.

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Nondecreasing and piecewise-continuous => piecewise-continuously-differentiable?

I'm interested to know if a piecewise-continuous monotone function from $\mathbb{R}$ to $\mathbb{R}$ is also piecewise-continuously differentiable. I mean piecewise in the sense that there is a finite ...
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Can i represent derivative as Lipschitz constant, if a function defined on interval (a,b]?

I am working with some piecewise linear functions and its' intervals defined as $I_j$=($x_j$,$x_{j+1}$]. I want to use the derivatives of sub-functions as Lipschitz constants, but in order to do that, ...
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Proving the integration of piecewise cubic functions as 0

Given that $g(x)$ is a piecewise cubic function, and $h(x) = \bar g(x)-g(x)$. I am struggling to show that $\sum_{i=1}^{N}\int_{x_{n-1}}^{x_n}g'''(x)h'(x)dx = 0$ I understand that $g'''(x)$ will be a ...
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Considerations when creating piecewise functions

I am asking about the dos and don'ts of piecewise expressions. First of all, there's the question of completeness versus clarity. Being as complete as possible can lead to long piecewise expressions ...