Respuesta :

mathstudent55

Answer:

9

Step-by-step explanation:

[tex] average~rate~of~change = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1} [/tex]

[tex] x_1 = 0 [/tex]

[tex] x_2 = 2 [/tex]

[tex] f(x_1) = f(0) = 0^2 + 7(0) + 10 = 10 [/tex]

[tex] f(x_2) = f(2) = 2^2 + 7(2) + 10 = 4 + 14 + 10 = 28 [/tex]

[tex] average~rate~of~change = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1} [/tex]

[tex] average~rate~of~change = \dfrac{28 - 10}{2 - 0} [/tex]

[tex] average~rate~of~change = \dfrac{18}{2} [/tex]

[tex] average~rate~of~change = 9 [/tex]

Answer:

9

Step-by-step explanation:

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

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

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 = [tex]\frac{28-10}{2-0}[/tex] = [tex]\frac{18}{2}[/tex] = 9

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