Question

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

Answer 1

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.