find the average rate of change of f(x)=2x² - 7x from x = 2 to x = 6. simplify your answer as much as…
find the average rate of change of f(x)=2x² - 7x from x = 2 to x = 6. simplify your answer as much as possible.
Answer
Answer:
7
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 $f(x)=2x^{2}-7x$.
Step2: Calculate $f(2)$
Substitute $x = 2$ into $f(x)$: $f(2)=2\times2^{2}-7\times2=2\times4 - 14=8 - 14=-6$.
Step3: Calculate $f(6)$
Substitute $x = 6$ into $f(x)$: $f(6)=2\times6^{2}-7\times6=2\times36-42 = 72 - 42=30$.
Step4: Calculate the average rate of change
$\frac{f(6)-f(2)}{6 - 2}=\frac{30-(-6)}{4}=\frac{30 + 6}{4}=\frac{36}{4}=7$.