The function is .

Definition of absolute value of the function :

If  , then and if , then .

when .

when .

Therefore the function can be written in piecewise form as

(a) Graph:

Graph the piecewise function.

 (b) Observe the graph,

For all values of , the function is differentiable.

(c) .

Derivative of the function is .

For ,

For ,

.

 (a)

(b) For all .

(c) .