calculate the average rate of change of the function over the given interval. f(x)=\\(\\sqrt3{x}\\); 5≤x≤11…

calculate the average rate of change of the function over the given interval. f(x)=\\(\\sqrt3{x}\\); 5≤x≤11 the average rate of change of f(x) over 5≤x≤11 is. (type an integer or decimal rounded to the nearest thousandth as needed.)

calculate the average rate of change of the function over the given interval. f(x)=\\(\\sqrt3{x}\\); 5≤x≤11 the average rate of change of f(x) over 5≤x≤11 is. (type an integer or decimal rounded to the nearest thousandth as needed.)

Answer

Explanation:

Step1: Definir la fórmula

La fórmula para el cambio promedio de una función $y = f(x)$ en el intervalo $[a,b]$ es $\frac{f(b)-f(a)}{b - a}$. Aquí, $a = 5$, $b=11$ y $f(x)=\sqrt[3]{x}$.

Step2: Calcular $f(11)$ y $f(5)$

$f(11)=\sqrt[3]{11}\approx2.224$ y $f(5)=\sqrt[3]{5}\approx1.710$.

Step3: Aplicar la fórmula

$\frac{f(11)-f(5)}{11 - 5}=\frac{\sqrt[3]{11}-\sqrt[3]{5}}{6}\approx\frac{2.224 - 1.710}{6}=\frac{0.514}{6}\approx0.086$.

Answer:

$0.086$