Explain in words why the instantaneous rate of change of the function f(x)=|x| cannot be determined at point (0,0)

Question

anonymous · Answer

because it has a nice corner there

anonymous · Answer

|dw:1361329753411:dw|

anonymous · Answer

rate of change for $x<0$ is always $-1$ and for $x>0$ it is always $1$

buggiethebug · Answer

but it is asking for the instantaneous rate of change?, is it because it's a cusp

anonymous · Answer

because on one side it is minus one (always) and on the other side it is one

anonymous · Answer

i guess you can say it is a "cusp"
instantaneous rate of change is the derivative right?

anonymous · Answer

absolute value is a piecewise function 
$$ = |x| = \left\{\begin{array}{rcc}
-x & \text{if}  & x \leq 0 \
x& \text{if}  & x >0
\end{array}
\right.
$$

buggiethebug · Answer

isnt it still approaching 0 from both sides.. doesnt that mean that there is a limit

buggiethebug · Answer

you are awesome thank youuu :3