Derivative of max(u(x),v(x))

  • Thread starter Dansuer
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  • #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
 

Answers and Replies

  • #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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Try looking at the two cases when u(x)>v(x) and when v(x)>u(x)
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
 
  • #4
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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.

For example
u(x) = 0 when x is rational, u(x) = 1 otherwise
v(x) = 1 when x is rational , v(x) = 0 otherwise
Or max(u(x),v(x)) can not be differentiable, while u(x) and v(x) are:

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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