Question

What is the average rate of change of   



`f(x)=x^{2}-x+4`



from `x=2` to  `x=4` ?

Answer 1

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 \( f(4) \).

1. **Calculate \( f(2) \):**
\[
f(2) = (2)^2 - (2) + 4 = 4 - 2 + 4 = 6
\]

2. **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 \( \boxed{5} \).