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- Thread starter Mr Davis 97
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- #2

BvU

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You already did. ##f(0)=\pm 1## and there is a differential equation

- #3

mfb

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Piecewise continuous examples include functions like

##f(x) = \left\{\begin{array}{c} 2^x, \hspace{30pt} |x|<5\\3^x, \hspace{30pt}|x|\geq 5\end{array}\right.##

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BvU

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mfb

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If f(x) for x>0 is differentiable and the limit of the derivative for x->0 is finite then I would expect f(x) to be differentiable everywhere.

This works both for real and complex function values.

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Svein

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[itex]f(x)=x^{2n} [/itex], [itex] f(x)=\lvert x \rvert[/itex], [itex]f(x)= \cos(\pi x) [/itex],...

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BvU

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Huh ?

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Svein

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- #11

jbriggs444

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Right. It is a special case of ##f(x)=k^x## which was mentioned in post #1 ("all exponential functions").But then the constant function [itex]f(x)=1 [/itex] is a trivial solution.

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Svein

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Another trivial solution is [itex]f(x)=-1 [/itex]...Right. It is a special case of ##f(x)=k^x## which was mentioned in post #1 ("all exponential functions").

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