Compute the average rate of change *f*(*x*) = 

*sqrt x*

 on the interval [9,9.06].


Round your answer to four decimal places.
Average rate of change = 

The average rate of change of a function \( f(x) \) on the interval \([a, b]\) is given by the formula:

\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]

In this case, \( f(x) = \sqrt{x} \), and the interval is \([9, 9.06]\).

1. Compute \( f(9) = \sqrt{9} = 3 \).
2. Compute \( f(9.06) = \sqrt{9.06} \).

Now, let's calculate:

\[
f(9.06) = \sqrt{9.06} \approx 3.0100
\]

Now apply the formula for the average rate of change:

\[
\text{Average rate of change} = \frac{f(9.06) - f(9)}{9.06 - 9}
\]
\[
\text{Average rate of change} = \frac{3.0100 - 3}{9.06 - 9} = \frac{0.0100}{0.06} \approx 0.1667
\]

Thus, the average rate of change is approximately:

\[
\boxed{0.1667}
\]

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. What is the general formula for the average rate of change of any function?
2. How does the average rate of change relate to the slope of a secant line?
3. What happens to the average rate of change as the interval shrinks?
4. Can we find the instantaneous rate of change at a point using limits?
5. How is the average rate of change different from the derivative?

**Tip:** The average rate of change over an interval gives you the slope of the secant line through the points on the graph at the interval's endpoints.

Compute the average rate of change f(x) = sqrt(x) on the interval [9, 9.06]. Round your answer to four decimal places.

Find the average rate of change of the function f(x) = sqrt(x) on the interval [9, 9.06]. This problem involves using the formula for the average rate of change to calculate the slope of the secant line between two points. Ideal for high school students in Grades 10-12.

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