https://file.aiquickdraw.com/mathbot/file/17300712540160njfv7i8.jpg

To determine the average rate of change of \( f \) over the interval \([1, 5]\), we can use the formula for the average rate of change:

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

where:
- \( a = 1 \)
- \( b = 5 \)
- \( f(1) = 2 \)
- \( f(5) = 14 \)

Plugging in the values:

\[
\frac{f(5) - f(1)}{5 - 1} = \frac{14 - 2}{5 - 1} = \frac{12}{4} = 3
\]

Thus, the average rate of change of \( f \) over the interval \([1, 5]\) is \( 3 \).

### Answer:
The correct choice is **C**: \(\frac{14 - 2}{5 - 1}\).

Would you like more details or have any questions?

### Related Questions:
1. What is the average rate of change of \( f \) over a different interval, such as \([2, 4]\)?
2. How would the result change if \( f(5) \) were a different value?
3. How can the average rate of change be interpreted graphically?
4. What is the significance of the interval endpoints \([1, 5]\) in this context?
5. How does average rate of change differ from instantaneous rate of change?

### Tip:
When finding the average rate of change, remember it essentially measures the "slope" between two points on the function's graph over a specified interval.

Selected values of a function f are shown in the table above. What is the average rate of change of f over the interval [1, 5]?

Learn how to calculate the average rate of change of a function over a specified interval. This problem demonstrates the use of the average rate of change formula with a function table. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation