Linear zigzag function
Graph of a piecewise linear zigzag function. For , we define the function  as follows:
1. For . 
    a. , if .
    b. , if .
2. For  .
    a. , if .
    b. , if .
3. Finally for , .
1. Prove that the function has a local minimum at 0.
2. What can you say about the notion of local maximum?
3. Is the function increasing or decreasing?