Let () be the piecewise linear function with domain 0≤≤8 shown in the graph below (which is determined by connecting the dots). Define a function () with domain 0≤≤8 by ()=∫0().

Notice that () is the net area under the function () for 0≤≤. If you click on the graph below, a full-size picture of the graph will open in another window.

Graph of =()

(A) Find the following values of the function ().
(0)=

(1)=

(2)=

(3)=

(4)=

(5)=

(6)=

(7)=

(8)=

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

() is decreasing for in the interval

(C) Find where () has its maximum and minimum values.
() has its maximum value when =

() has its minimum value when =