10 the average rate of change of $f(x)=x^{2}-x + 4$ from $x = 2$ to $x = 4$ is\na 10\nb 5\nc 3\nd 2
10 the average rate of change of $f(x)=x^{2}-x + 4$ from $x = 2$ to $x = 4$ is\na 10\nb 5\nc 3\nd 2
Answer
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