select the correct answer. what is the average rate of change of f(x), represented by the table of values…

select the correct answer. what is the average rate of change of f(x), represented by the table of values, over the interval -3, 4? x f(x) -6 27 -3 6 -1 2 0 3 1 6 4 27 a. -6 b. -3 c. 3 d. 6 e. 21

select the correct answer. what is the average rate of change of f(x), represented by the table of values, over the interval -3, 4? x f(x) -6 27 -3 6 -1 2 0 3 1 6 4 27 a. -6 b. -3 c. 3 d. 6 e. 21

Answer

Explanation:

Step1: Identificar los valores de x y f(x)

Para el intervalo [-3, 4], cuando x = - 3, f(-3)=6 y cuando x = 4, f(4)=27.

Step2: Aplicar la fórmula del cambio promedio

La fórmula para el cambio promedio de una función f(x) en el intervalo [a, b] es $\frac{f(b)-f(a)}{b - a}$. Aquí, a=-3, b = 4, f(a)=6 y f(b)=27. Entonces $\frac{f(4)-f(-3)}{4-(-3)}=\frac{27 - 6}{4 + 3}$.

Step3: Realizar los cálculos

$\frac{27 - 6}{4 + 3}=\frac{21}{7}=3$.

Answer:

C. 3