Question

find the average rate of change of the function over the interval 4,11.
$f(x)=\frac{60}{2x - 2}$
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Explanation:

Step1: Definir la fórmula

La tasa media de cambio de una función $y = f(x)$ en el intervalo $[a,b]$ es $\frac{f(b)-f(a)}{b - a}$. Aquí, $a = 4$, $b=11$ y $f(x)=\frac{60}{2x - 2}$.

Step2: Calcular $f(4)$

Sustituir $x = 4$ en $f(x)$:
$f(4)=\frac{60}{2\times4-2}=\frac{60}{8 - 2}=\frac{60}{6}=10$.

Step3: Calcular $f(11)$

Sustituir $x = 11$ en $f(x)$:
$f(11)=\frac{60}{2\times11-2}=\frac{60}{22 - 2}=\frac{60}{20}=3$.

Step4: Calcular la tasa media de cambio

$\frac{f(11)-f(4)}{11 - 4}=\frac{3 - 10}{7}=\frac{-7}{7}=- 1$.

Answer:

$-1$