Question

Calculate the average rate of change over the interval [3,4] of the given graph of the function. f(X) (3,4) (4,20)

Answer 1

To calculate the average rate of change of a function \( f(x) \) over the interval \([a, b]\), we use the formula:

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

For your given points, we have:

- At \( x = 3 \), \( f(3) = 4 \)
- At \( x = 4 \), \( f(4) = 20 \)

Now, let's apply these values into the formula where \( a = 3 \) and \( b = 4 \):

\[
\text{Average Rate of Change} = \frac{f(4) - f(3)}{4 - 3} = \frac{20 - 4}{4 - 3} = \frac{16}{1} = 16
\]

So, the average rate of change of the function \( f(x) \) over the interval \([3, 4]\) is \( 16 \).