Question

Find the average rate of change for f(x) = x2 + 9x + 18 from x = −10 to x = 10.

Answer 1

The average rate of change formula is 
           f(b) - f(a)
arc = ----------------
               b-a
                    
Here, a= -10 and b = 10

                   (10)^2 + 9(10) + 18 - [ (-10)^2 + 9(-10) + 18]
Here arc = --------------------------------------------------------------
                                     10 - (-10)

10^2 and -(-10)^2 cancel.     18 - 18 cancel.

                                               90 - (-90)            180
This leaves us with     arc = ----------------- = ------------- = 9 (answer)
                                                   20                     20