Question

9 the average rate of change of ( f(x) = x^2 - x + 4 ) from ( x = 2 ) to ( x = 4 ) is
a 10
b 5
c 3
d 2

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) from \( x = a \) to \( x = b \) is given by \( \frac{f(b)-f(a)}{b - a} \). Here, \( a = 2 \), \( b = 4 \), and \( f(x)=x^{2}-x + 4 \).

Step2: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x) \):
\( f(2)=(2)^{2}-2 + 4=4-2 + 4=6 \)

Step3: Calculate \( f(4) \)

Substitute \( x = 4 \) into \( f(x) \):
\( f(4)=(4)^{2}-4 + 4=16-4 + 4=16 \)

Step4: Calculate the average rate of change

Using the formula \( \frac{f(4)-f(2)}{4 - 2} \), substitute \( f(4)=16 \) and \( f(2)=6 \):
\( \frac{16 - 6}{4 - 2}=\frac{10}{2}=5 \)

Answer:

B. 5