Question

question 7
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calculate the average rate of change of $f(x)=\sqrt{x+5}$ on the interval $-4,4$.
$\frac{1}{2}$
$\frac{1}{4}$
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$-\frac{1}{4}$

Explanation:

Step1: Recall average rate of change formula

The average rate of change of $f(x)$ on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Calculate $f(-4)$

$f(-4)=\sqrt{-4+5}=\sqrt{1}=1$

Step3: Calculate $f(4)$

$f(4)=\sqrt{4+5}=\sqrt{9}=3$

Step4: Compute average rate of change

Substitute values: $\frac{f(4)-f(-4)}{4-(-4)}=\frac{3-1}{4+4}=\frac{2}{8}=\frac{1}{4}$

Answer:

B. $\frac{1}{4}$