Find the average rate of change for f(x) = x2 − 3x − 10 from x = 4 to x = 6

I believe you meant f(x) = x^2 - 3x - 10.
                                                              f(b) - f(a)
The ave. r. of c. formula is     a. r. c =
                                                                 b -a
                               (6)^2 - 3(6) - 10 - [(4)^2 - 3(4) - 10]
Here,   a. r. c. =          
                                                      6-4
                                           36 - 18 -10 - 16 + 12 + 10
     ... which comes out to
                                                                2

                a. r. c. = 7             for x^2 - 3x - 10 on the interval [4,6]

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