i am given two differentiable function f and g .

prove that for u(x)=max(f(x),g(x))

and v(x)=min(f(x),g(x))

there is one sided derivatives

??

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- Jan 21st 2009, 01:24 PMtransgalacticone sided differentiation prove..
i am given two differentiable function f and g .

prove that for u(x)=max(f(x),g(x))

and v(x)=min(f(x),g(x))

there is one sided derivatives

?? - Jan 23rd 2009, 11:35 PMtransgalactic
whats a one sided derivative

- Jan 23rd 2009, 11:40 PMJhevon
i suppose it is the derivative found by taking either the right- or left-hand limit.

that is:

$\displaystyle f'(x) = \lim_{h \to 0} \frac {f(x + h) - f(x)}h$ (the derivative)

$\displaystyle f'(x)_+ = \lim_{h \to 0^+} \frac {f(x + h) - f(x)}h$ (one-sided derivative...from the right)

$\displaystyle f'(x)_- = \lim_{h \to 0^-} \frac {f(x + h) - f(x)}h$ (one-sided derivative... from the left) - Jan 23rd 2009, 11:42 PMtransgalactic
how to put mim ,max functions into this limit formula??

- Jan 25th 2009, 06:21 AMtransgalactic
deffentiable function is a function which on soome point its

left side derivative equals its write side derivative.

so

if both functions are derivatable.

then it doent matter what function we take

there for sure will be a function where

it has a point for which there is a derivative on both sides

even though we need only one.

so its an over kill

am i correct?