Question
Calculate the average rate of change over the interval [3,4] of the given graph of the function with the following points on the graph:(3, 4), (4, 20)
Answers
GPT-4o mini
To calculate the average rate of change of a function over an interval \([a, b]\), you can use the formula:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
In your case, you have the points \((3, 4)\) and \((4, 20)\). Here, \(a = 3\), \(b = 4\), \(f(a) = 4\), and \(f(b) = 20\).
Now, plug these values into the formula:
\[
\text{Average Rate of Change} = \frac{20 - 4}{4 - 3} = \frac{16}{1} = 16
\]
Therefore, the average rate of change of the function over the interval \([3, 4]\) is \(16\).
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
In your case, you have the points \((3, 4)\) and \((4, 20)\). Here, \(a = 3\), \(b = 4\), \(f(a) = 4\), and \(f(b) = 20\).
Now, plug these values into the formula:
\[
\text{Average Rate of Change} = \frac{20 - 4}{4 - 3} = \frac{16}{1} = 16
\]
Therefore, the average rate of change of the function over the interval \([3, 4]\) is \(16\).