https://file.aiquickdraw.com/mathbot/file/1727884155321rcnpqboq.jpg

The problem asks for the average rate of change of the function \( y = \sqrt{2x - 1} \) over the interval from \( x = 5 \) to \( x = 13 \).

The average rate of change of a function \( f(x) \) between two points \( x = a \) and \( x = b \) is given by the formula:

\[
\frac{f(b) - f(a)}{b - a}
\]

Here, the function is \( f(x) = \sqrt{2x - 1} \), and the points are \( x = 5 \) and \( x = 13 \).

So, we need to compute:

\[
\frac{f(13) - f(5)}{13 - 5}
\]

This matches option **C** in the question:

\[
\frac{f(13) - f(5)}{13 - 5}
\]

Thus, the correct answer is **C**.

Would you like to go over the detailed steps for finding \( f(13) \) and \( f(5) \) to calculate the average rate of change? Let me know if you have any questions!

Here are 5 related questions for further exploration:

1. What is the difference between the average rate of change and the instantaneous rate of change?
2. How would you find the derivative of the function \( f(x) = \sqrt{2x - 1} \)?
3. What does the average rate of change represent geometrically on the graph of a function?
4. How would the average rate of change change if the interval were \( x = 7 \) to \( x = 13 \)?
5. Can the average rate of change be negative? If yes, what does that indicate?

**Tip:** The average rate of change is the slope of the secant line passing through two points on the function.

Find the average rate of change of the function y = √(2x − 1) over the interval from x = 5 to x = 13. What expression can be used to find the average rate of change?

Learn how to calculate the average rate of change of the function y = √(2x − 1) over the interval from x = 5 to x = 13. Understand the formula for average rate of change and its geometric interpretation as the slope of the secant line.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation