Find the average rate of change of the function from to .
The average rate of change is . (Simplify your answer.)

Ask by John Olson. in the United States

Jan 24,2025

Question

Find the average rate of change of the function $$ f(x)=\sqrt{x} $$ from $$ x_{1}=4 $$ to $$ x_{2}=49 $$. The average rate of change is $$ \square $$. (Simplify your answer.)

UpStudy AI · Accepted Answer

The average rate of change of the function $$ f(x) = \sqrt{x} $$ from $$ x_1 = 4 $$ to $$ x_2 = 49 $$ is calculated using the formula:

$$
\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
$$

First, compute $$ f(x_1) $$ and $$ f(x_2) $$:

$$
f(4) = \sqrt{4} = 2
$$
$$
f(49) = \sqrt{49} = 7
$$

Now, substitute these values into the formula:

$$
\text{Average Rate of Change} = \frac{7 - 2}{49 - 4} = \frac{5}{45} = \frac{1}{9}
$$

**Answer:** $$\boxed{\dfrac{1}{9}}$$
The average rate of change is $$\frac{1}{9}$$.

Find the average rate of change of the function from to .
The average rate of change is . (Simplify your answer.)

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Find the average rate of change of the function from to . The average rate of change is . (Simplify your answer.)