How do I find the equation of f '(x) using the newton quotient equation.

f(x) = |x-6|

Question

How do I find the equation of f '(x) using the newton quotient equation.

f(x) = |x-6|

agentjamesbond007 · Answer

lim f(x+h) - f(x)
x->0

anonymous · Answer

f'(x)=lim [|(x+h)-6|-|x-6|]/h
       x->0

agentjamesbond007 · Answer

So does it end up at

lim h/h
h ->0

If that is so, would that be 1 or 0/0?

anonymous · Answer

you need two cases, one for $x>6$ and one for $x<6$

anonymous · Answer

it is absolute value, right?

agentjamesbond007 · Answer

ah, so I have to break it up into a piecewise function?

anonymous · Answer

yes because 
$$f(x)= |x-6| = \left\{\begin{array}{rcc}
-x+6 & \text{if}  & x <x \
x-6& \text{if}  & x\geq 6
\end{array}
\right.$$

anonymous · Answer

in any case the answer you should get is simple, because these are just two line.. slope of first one is $-1$ and slope of second one is $1$