Question

10 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 average - rate - of - change formula

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

Step2: Calculate $f(4)$

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

Step3: Calculate $f(2)$

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

Step4: Calculate the average rate of change

$\frac{f(4)-f(2)}{4 - 2}=\frac{16 - 6}{2}=\frac{10}{2}=5$.

Answer:

B. 5