Question

Calculate the average rate of change of the quadratic function y = -x2 + 4x +2

over the interval 0 to 2.​

Answer 1

2

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 ] = [ 0, 2 ], thus

f(b) = f(2) = -(2)² + 4)(2) + 2 = - 4 + 8 + 2 = 6

f(a) = f(0) = 2

average rate of change =
`(6-2)/(2-0)` =
`(4)/(2)` = 2