To find the average rate of change of the function \( f(x) = x^2 - x + 4 \) from \( x = 2 \) to \( x = 4 \), we use the formula for the average rate of change:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = 2 \) and \( b = 4 \).
First, we calculate \( f(2) \) and \( f(4) \).
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Calculate \( f(2) \): \[ f(2) = (2)^2 - (2) + 4 = 4 - 2 + 4 = 6 \]
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Calculate \( f(4) \): \[ f(4) = (4)^2 - (4) + 4 = 16 - 4 + 4 = 16 \]
Now, we can substitute these values into the average rate of change formula:
\[ \text{Average Rate of Change} = \frac{f(4) - f(2)}{4 - 2} = \frac{16 - 6}{4 - 2} = \frac{10}{2} = 5 \]
Thus, the average rate of change of \( f(x) \) from \( x = 2 \) to \( x = 4 \) is \( \boxed{5} \).