Question

If AX) = x2 + 2x + 3, what is the average rate of change of AX) over the interval (-4, 6]? OA 51 B. 40 OC. 31 OD 20 OE 4​

Answer 1

E

Explanation:

The average rate of change of A(x) in the closed interval [ a, b ] is

`(f(b)-f(a))/(b-a)`

Here [ a, b ] = [ - 4, 6 ] , then

f(b) = f(6) = 6² + 2(6) + 3 = 36 + 12 + 3 = 51

f(a) = f(- 4) = (- 4)² + 2(- 4) + 3 = 16 - 8 + 3 = 11 , thus

average rate of change =
`(51-11)/(6-(-4))` =
`(40)/(10)` = 4 → E