Respuesta :

Answer: C(x) > a(x) , meaning c(X) has the greatest average rate of change over the given interval.

Explanations :

• The greatest average rate of change = slope

,

• given by formula :

[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]

(a) For a(x),

[tex]\begin{gathered} minitial\text{ = }\frac{-2+3\text{ }}{0+1\text{ }} \\ \text{ = 1/1} \\ \text{ = 1 } \end{gathered}[/tex][tex]\begin{gathered} m\text{ final = }\frac{13-6}{3-2} \\ \text{ = }7\text{ } \end{gathered}[/tex]

• The average rate of change over the given interval = 7-1 = 6

(b) for b(x) , we have

[tex]\begin{gathered} M\text{ initial = }\frac{3-1}{0+1} \\ \text{ = 2} \end{gathered}[/tex]

and

[tex]\begin{gathered} m\text{ final = }\frac{9-7\text{ }}{3-2\text{ }} \\ \text{ = 2} \end{gathered}[/tex]

• We can see that b(x) has constant average rate of change at 2 , therefore this will not be considered for this purpose of the exercise.

(c) for C(x) , we have

[tex]\begin{gathered} M\text{ initial = }\frac{-1+2}{0+1} \\ \text{ = 1 } \end{gathered}[/tex]

and

[tex]\begin{gathered} m\text{ final = }\frac{13-5\text{ }}{3-2} \\ \text{ = }8\text{ } \end{gathered}[/tex]

• The average rate of change over the given interval =, 8 -1 = 7

in conclusion , C(x) = 7 , whereas a(x) = 6 ,

Therfore C(x) > a(x)

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