Pregunta
Find the average rate of change of the function \( f(x)=\sqrt{x} \) from \( x_{1}=100 \) to \( x_{2}=121 \). The average rate of change is \( \square \). (Simplify your answer.)
Ask by Wright Fernandez. in the United States
Mar 09,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The average rate of change is \( \frac{1}{21} \).
Solución
1. The average rate of change of a function \( f(x) \) from \( x_1 \) to \( x_2 \) is given by:
\[
\frac{f(x_2)-f(x_1)}{x_2-x_1}
\]
2. For \( f(x)=\sqrt{x} \), compute:
\[
f(121) = \sqrt{121} = 11 \quad \text{and} \quad f(100) = \sqrt{100} = 10.
\]
3. Substitute these values into the formula:
\[
\frac{f(121)-f(100)}{121-100} = \frac{11-10}{21} = \frac{1}{21}.
\]
The average rate of change is \( \frac{1}{21} \).
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Simplifique esta solución Extra Insights
To find the average rate of change of the function \( f(x) = \sqrt{x} \) from \( x_1 = 100 \) to \( x_2 = 121 \), we use the formula: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] First, calculate \( f(x_1) \) and \( f(x_2) \): \[ f(100) = \sqrt{100} = 10 \] \[ f(121) = \sqrt{121} = 11 \] Now, substitute these values into the formula: \[ \text{Average Rate of Change} = \frac{11 - 10}{121 - 100} = \frac{1}{21} \] Thus, the average rate of change is \( \frac{1}{21} \).
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