Question

Calculate the average rate of change of f(x) = x2/4 - 5 for 3 ≤ x ≤ 5. A) -2 B) -4/3 C) 4/3 D) 2

Answer 1

Answer: The answer is 2

Answer 2

D

Explanation:

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

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

here [ a, b ] = [ 3, 5 ]

f(b) = f(5) =
`(5^(2) )/(4)` - 5 =
`(25)/(4)` -
`(20)/(4)` =
`(5)/(4)`

f(a) = f(3) =
`(3^(2) )/(4)` - 5 =
`(9)/(4)` -
`(20)/(4)` = -
`(11)/(4)`

Hence

average rate of change =
`(5/4+11/4)/(5-3)` =
`(4)/(2)` = 2