Question

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

Answer 1

Answer:

9

Step-by-step explanation:

$average~rate~of~change = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1}$

$x_1 = 0$

$x_2 = 2$

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

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

$average~rate~of~change = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1}$

$average~rate~of~change = \dfrac{28 - 10}{2 - 0}$

$average~rate~of~change = \dfrac{18}{2}$

$average~rate~of~change = 9$

Answer 2

Answer:

9

Step-by-step explanation:

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

$\frac{f(b)-f(a)}{b-a}$

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 = $\frac{28-10}{2-0}$ = $\frac{18}{2}$ = 9