Question

calculate the average rate of change for the function, f(x)=4\sqrt{x}-3 over the interval 4,9

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$, $b = 9$, and $f(x)=4\sqrt{x}-3$.

Step2: Calculate $f(4)$

Substitute $x = 4$ into $f(x)$: $f(4)=4\sqrt{4}-3=4\times2 - 3=8 - 3=5$.

Step3: Calculate $f(9)$

Substitute $x = 9$ into $f(x)$: $f(9)=4\sqrt{9}-3=4\times3 - 3=12 - 3=9$.

Step4: Calculate the average rate of change

Use the formula $\frac{f(9)-f(4)}{9 - 4}=\frac{9 - 5}{9 - 4}=\frac{4}{5}$.

Answer:

$\frac{4}{5}$