Bot GPT 4-o mini To find the average rate of change of the function \( f(x) = x^2 + 9x + 18 \) from \( x = 10 \) to \( x = 20 \), we will use the formula for the average rate of change:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = 10 \) and \( b = 20 \).
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First, calculate \( f(10) \): \[ f(10) = 10^2 + 9(10) + 18 = 100 + 90 + 18 = 208 \]
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Next, calculate \( f(20) \): \[ f(20) = 20^2 + 9(20) + 18 = 400 + 180 + 18 = 598 \]
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Now substitute \( f(10) \) and \( f(20) \) into the average rate of change formula: \[ \text{Average Rate of Change} = \frac{f(20) - f(10)}{20 - 10} = \frac{598 - 208}{10} = \frac{390}{10} = 39 \]
Thus, the average rate of change of the function \( f(x) \) from \( x = 10 \) to \( x = 20 \) is \( 39 \).
Therefore, the correct answer is: C 39.
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