Question

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

f(x) = |x-6|

Answer 1

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

Answer 2

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

Answer 3

So does it end up at

lim h/h
h ->0

If that is so, would that be 1 or 0/0?

Answer 4

you need two cases, one for \(x>6\) and one for \(x<6\)

Answer 5

it is absolute value, right?

Answer 6

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

Answer 7

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

Answer 8

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 \(1\)