Question
g(x)=2-1 over the interval [2,3]. State the difference in the estimated average rates of nearest tenth.
Answers
GPT-4o mini
To find the estimated average rate of change of the function \( g(x) = 2 - x \) over the interval \([2, 3]\), we can use the formula for the average rate of change:
\[
\text{Average Rate of Change} = \frac{g(b) - g(a)}{b - a}
\]
where \( a = 2 \) and \( b = 3 \).
First, let's calculate \( g(2) \) and \( g(3) \):
\[
g(2) = 2 - 2 = 0
\]
\[
g(3) = 2 - 3 = -1
\]
Now, we can plug these values into the formula for the average rate of change:
\[
\text{Average Rate of Change} = \frac{g(3) - g(2)}{3 - 2} = \frac{-1 - 0}{3 - 2} = \frac{-1}{1} = -1
\]
Thus, the estimated average rate of change of the function \( g(x) = 2 - x \) over the interval \([2, 3]\) is \( -1.0 \) when rounded to the nearest tenth.
There is no other average rate specified for comparison in your question, so I can only report that the average rate is \( -1.0 \) over the given interval. If there is another interval or function for comparison, please provide that information!
\[
\text{Average Rate of Change} = \frac{g(b) - g(a)}{b - a}
\]
where \( a = 2 \) and \( b = 3 \).
First, let's calculate \( g(2) \) and \( g(3) \):
\[
g(2) = 2 - 2 = 0
\]
\[
g(3) = 2 - 3 = -1
\]
Now, we can plug these values into the formula for the average rate of change:
\[
\text{Average Rate of Change} = \frac{g(3) - g(2)}{3 - 2} = \frac{-1 - 0}{3 - 2} = \frac{-1}{1} = -1
\]
Thus, the estimated average rate of change of the function \( g(x) = 2 - x \) over the interval \([2, 3]\) is \( -1.0 \) when rounded to the nearest tenth.
There is no other average rate specified for comparison in your question, so I can only report that the average rate is \( -1.0 \) over the given interval. If there is another interval or function for comparison, please provide that information!