Question

Find the average rate of change for f (x)=x2+7x+10 from x=0 to x=2

Answer 1

9

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 ]

f(b) = f(2) = 2² + 7(2) + 10 = 4 + 14 + 10 = 28

f(a) = f(0) = 0 + 0 + 10 = 10, hence

average rate of change =
`(28-10)/(2-0)` =
`(18)/(2)` = 9

Answer 2

9

Explanation:

`average~rate~of~change = (f(x_2) - f(x_1))/(x_2 - x_1)`

`x_1 = 0`

`x_2 = 2`

`f(x_1) = f(0) = 0^2 + 7(0) + 10 = 10`

`f(x_2) = f(2) = 2^2 + 7(2) + 10 = 4 + 14 + 10 = 28`

`average~rate~of~change = (f(x_2) - f(x_1))/(x_2 - x_1)`

`average~rate~of~change = (28 - 10)/(2 - 0)`

`average~rate~of~change = (18)/(2)`

`average~rate~of~change = 9`