Question
Calculate the average rate of change over the interval [3,4]
of the given graph of the function.
3,4to 4,2what is the rate of change
of the given graph of the function.
3,4to 4,2what is the rate of change
Answers
GPT-4o mini
To calculate the average rate of change of a function over the interval \([3, 4]\), you can use the formula:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a = 3 \), \( b = 4 \), \( f(a) \) is the value of the function at \( a \), and \( f(b) \) is the value of the function at \( b \).
From your data, we have:
- \( f(3) = 4.2 \)
- \( f(4) = 4.0 \)
Now, plug these values into the formula:
\[
\text{Average Rate of Change} = \frac{f(4) - f(3)}{4 - 3} = \frac{4.0 - 4.2}{4 - 3} = \frac{-0.2}{1} = -0.2
\]
Thus, the average rate of change of the function over the interval \([3, 4]\) is \(-0.2\).
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a = 3 \), \( b = 4 \), \( f(a) \) is the value of the function at \( a \), and \( f(b) \) is the value of the function at \( b \).
From your data, we have:
- \( f(3) = 4.2 \)
- \( f(4) = 4.0 \)
Now, plug these values into the formula:
\[
\text{Average Rate of Change} = \frac{f(4) - f(3)}{4 - 3} = \frac{4.0 - 4.2}{4 - 3} = \frac{-0.2}{1} = -0.2
\]
Thus, the average rate of change of the function over the interval \([3, 4]\) is \(-0.2\).