one sided differentiation prove..

• Jan 21st 2009, 01:24 PM
transgalactic
one 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 PM
transgalactic
whats a one sided derivative
• Jan 23rd 2009, 11:40 PM
Jhevon
Quote:

Originally Posted by transgalactic
whats a one sided derivative

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 PM
transgalactic
how to put mim ,max functions into this limit formula??
• Jan 25th 2009, 06:21 AM
transgalactic
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?