let f(x)=x² + 5x - 8. what is the average rate of change from x = 2 to x = 6? enter your answer in the box.
let f(x)=x² + 5x - 8. what is the average rate of change from x = 2 to x = 6? enter your answer in the box.
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, $a = 2$, $b=6$, and $f(x)=x^{2}+5x - 8$.
Step2: Calculate $f(6)$
Substitute $x = 6$ into $f(x)$: $f(6)=6^{2}+5\times6 - 8=36 + 30-8=58$.
Step3: Calculate $f(2)$
Substitute $x = 2$ into $f(x)$: $f(2)=2^{2}+5\times2 - 8=4 + 10-8=6$.
Step4: Calculate the average rate of change
$\frac{f(6)-f(2)}{6 - 2}=\frac{58 - 6}{4}=\frac{52}{4}=13$.
Answer:
13