If f (x) = x2 + 2x + 3, what is the average rate of change of f (x) over the interval [-4, 6]?

A. 51

B. 40

C. 31

D. 20

E. 4

Calculating the value of f (x) for the given interval.

For x = - 4, f (x) = f ( - 4) = ( - 4) ^2 + 2 ( - 4) + 3 = 11

For x = 6, f (x) = f (6) = (6) ^2 + 2 (6) + 3 = 51

Now using formula for the calculation of average rate of change of f (x) over the given interval of [ - 4, 6];

(f (b) - f (a)) / b - a = (f (6) - f ( - 4)) / 6 - ( - 4) = (51 - 11) / 10 = 4

So option "E" is correct.