- #1

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## Main Question or Discussion Point

What is the derivative of the function f(x)= max(u(x),v(x)) ?

where u(x) and v(x) are two given function

where u(x) and v(x) are two given function

- Thread starter Dansuer
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- #1

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What is the derivative of the function f(x)= max(u(x),v(x)) ?

where u(x) and v(x) are two given function

where u(x) and v(x) are two given function

- #2

Office_Shredder

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Try looking at the two cases when u(x)>v(x) and when v(x)>u(x)

- #3

AlephZero

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That is a good place to start, but max(u(x),v(x)) can be differentiable when u(x) and v(x) are not even continuous.Try looking at the two cases when u(x)>v(x) and when v(x)>u(x)

For example

u(x) = 0 when x is rational, u(x) = 1 otherwise

v(x) = 1 when x is rational , v(x) = 0 otherwise

- #4

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Or max(u(x),v(x)) can not be differentiable, while u(x) and v(x) are:That is a good place to start, but max(u(x),v(x)) can be differentiable when u(x) and v(x) are not even continuous.

For example

u(x) = 0 when x is rational, u(x) = 1 otherwise

v(x) = 1 when x is rational , v(x) = 0 otherwise

For example:

u(x)=x and v(x)=-x

Then max(u(x),v(x))=|x| which is not differentiable in 0.

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