Question
Find the average rate of change of k(x)= – 6 x over the interval 0,2. Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions.
Answers
GPT-4o mini
To find the average rate of change of the function \( k(x) = -6x \) over the interval \([0, 2]\), we use the formula for the average rate of change:
\[
\text{Average rate of change} = \frac{k(b) - k(a)}{b - a}
\]
where \( a = 0 \) and \( b = 2 \).
First, we need to calculate \( k(0) \) and \( k(2) \):
\[
k(0) = -6(0) = 0
\]
\[
k(2) = -6(2) = -12
\]
Now we can substitute these values into the formula:
\[
\text{Average rate of change} = \frac{k(2) - k(0)}{2 - 0} = \frac{-12 - 0}{2 - 0} = \frac{-12}{2} = -6
\]
Thus, the average rate of change of \( k(x) \) over the interval \([0, 2]\) is \(\boxed{-6}\).
\[
\text{Average rate of change} = \frac{k(b) - k(a)}{b - a}
\]
where \( a = 0 \) and \( b = 2 \).
First, we need to calculate \( k(0) \) and \( k(2) \):
\[
k(0) = -6(0) = 0
\]
\[
k(2) = -6(2) = -12
\]
Now we can substitute these values into the formula:
\[
\text{Average rate of change} = \frac{k(2) - k(0)}{2 - 0} = \frac{-12 - 0}{2 - 0} = \frac{-12}{2} = -6
\]
Thus, the average rate of change of \( k(x) \) over the interval \([0, 2]\) is \(\boxed{-6}\).