Let [math] be the piecewise linear function with domain [math] shown in the graph below (which is determined by connecting the dots). Define a function [math] with domain [math] by

[math]
Notice that [math] is the net area under the function [math] for [math]. If you click on the graph below, a full-size picture of the graph will open in another window.

Graph of [math]


(A) Find the following values of the function [math].
[math]
[math]
[math]
[math]
[math]
[math]
[math]
[math]
[math]

(B) Use interval notation to indicate the interval or union of intervals where [math] is increasing and decreasing.
[math] is increasing for [math] in the interval
[math] is decreasing for [math] in the interval

(C) Find where [math] has its maximum and minimum values.
[math] has its maximum value when [math]
[math] has its minimum value when [math]

Solution: