QuestionAugust 24, 2025

Find the average rate of change of f(x)=(1)/(-4x) over the interval [-5,-1] Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions. square

Find the average rate of change of f(x)=(1)/(-4x) over the interval [-5,-1] Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions. square
Find the average rate of change of f(x)=(1)/(-4x) over the interval [-5,-1]
Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify
any fractions.
square

Solution
4.5(272 votes)

Answer

\frac{1}{20} Explanation 1. Calculate f(x) at endpoints f(-5) = \frac{1}{-4(-5)} = \frac{1}{20} and f(-1) = \frac{1}{-4(-1)} = \frac{1}{4}. 2. Use the average rate of change formula **Average Rate of Change** is given by \frac{f(b) - f(a)}{b - a}. Here, a = -5 and b = -1. 3. Substitute values into the formula \frac{\frac{1}{4} - \frac{1}{20}}{-1 + 5} = \frac{\frac{5}{20} - \frac{1}{20}}{4} = \frac{\frac{4}{20}}{4} = \frac{1}{20}.

Explanation

1. Calculate $f(x)$ at endpoints<br /> $f(-5) = \frac{1}{-4(-5)} = \frac{1}{20}$ and $f(-1) = \frac{1}{-4(-1)} = \frac{1}{4}$.<br />2. Use the average rate of change formula<br /> **Average Rate of Change** is given by $\frac{f(b) - f(a)}{b - a}$. Here, $a = -5$ and $b = -1$.<br />3. Substitute values into the formula<br /> $\frac{\frac{1}{4} - \frac{1}{20}}{-1 + 5} = \frac{\frac{5}{20} - \frac{1}{20}}{4} = \frac{\frac{4}{20}}{4} = \frac{1}{20}$.
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