given $f(x)=17 - x^{2}$, what is the average rate of change in $f(x)$ over the interval $1,5$?\n-6\n$-\frac{1…

given $f(x)=17 - x^{2}$, what is the average rate of change in $f(x)$ over the interval $1,5$?\n-6\n$-\frac{1}{2}$\n$\frac{1}{4}$\n1

given $f(x)=17 - x^{2}$, what is the average rate of change in $f(x)$ over the interval $1,5$?\n-6\n$-\frac{1}{2}$\n$\frac{1}{4}$\n1

Answer

Explanation:

Step1: Encontrar f(1)

Sustituir x = 1 en f(x)=17 - x². f(1)=17 - 1²=17 - 1 = 16

Step2: Encontrar f(5)

Sustituir x = 5 en f(x)=17 - x². f(5)=17 - 5²=17 - 25=-8

Step3: Aplicar la fórmula de tasa de cambio promedio

La fórmula para la tasa de cambio promedio de una función f(x) en el intervalo [a, b] es $\frac{f(b)-f(a)}{b - a}$. Aquí, a = 1, b = 5, f(1)=16 y f(5)=-8. $\frac{f(5)-f(1)}{5 - 1}=\frac{-8 - 16}{4}=\frac{-24}{4}=-6$

Answer:

A. -6