Question

What is the average rate of change of the functionf(x) = 2x² - 5x on the interval [2, 4]?

The average rate of change is______

Answer 1

7

Explanation:

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

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

here [ a, b ] = [ 2, 4 ] , then

f(b) = f4) = 2(4)² - 5(4) = 2(16) - 20 = 32 - 20 = 12

f(a) = f(2) = 2(2)² - 5(2) = 2(4) - 10 = 8 - 10 = - 2 , then

average rate of change =
`(12-(-2))/(4-2)` =
`(12+2)/(2)` =
`(14)/(2)` = 7