If f(x)=x^3-x, what is the average rate of change of f(x) over the interval [1, 5]?

The question is basically asking you to make a straight line between those two points and find its gradient.

The first step youd best take is to find the coordinates of the points needed so:
f(1)=1^3-1 .               f(5)=5^3-5
     =0                              =120
therefore coordinates are:
  (1,0) and (5,120)

the general form of a gradient is:
m=(y2-y1)/(x2-x1)

so plug in your values and you get 
m=(120-0)/(5-1)
   =120/4
   = 30

so your average rate of change between those two values is 30

Hopefully this has been clear enough, good luck

What are the following algebraic equations. you need to post those if you want the answer