Question

Calculate the average rate of change of the function f(x) = 3x2 over the interval 1 ≤ x ≤ 5.

Answer 1

Answer:18

Explanation:

here [ a, b ] = [ 1, 5 ]

f(b) = f(5) = 3 × 5² = 75

f(a) = f(1) = 3 × 1² = 3, hence

average rate of change = = = 18

Answer 2

18

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 ] = [ 1, 5 ]

f(b) = f(5) = 3 × 5² = 75

f(a) = f(1) = 3 × 1² = 3, hence

average rate of change =
`(75-3)/(5-1)` =
`(72)/(4)` = 18