Question

10 numeric 10 points calculate the average rate of change for the function, $f(x)=3sqrt{x}+2$ on the interval $1,4$ answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 4$, and $f(x)=3\sqrt{x}+2$.

Step2: Calculate $f(4)$

Substitute $x = 4$ into $f(x)$: $f(4)=3\sqrt{4}+2=3\times2 + 2=6 + 2=8$.

Step3: Calculate $f(1)$

Substitute $x = 1$ into $f(x)$: $f(1)=3\sqrt{1}+2=3\times1+2=3 + 2=5$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(4)-f(1)}{4 - 1}$, we substitute $f(4)=8$ and $f(1)=5$: $\frac{8 - 5}{4 - 1}=\frac{3}{3}=1$.

Answer:

$1$