find the average rate of change of f(x)=2x² - 9x from x = 2 to x = 6. simplify your answer as much as…

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 $f(x)=2x^{2}-9x$.

Step2: Calculate $f(6)$

Substitute $x = 6$ into $f(x)$: $f(6)=2\times6^{2}-9\times6=2\times36 - 54=72 - 54 = 18$.

Step3: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$: $f(2)=2\times2^{2}-9\times2=2\times4-18 = 8 - 18=-10$.

Step4: Calculate the average rate of change

$\frac{f(6)-f(2)}{6 - 2}=\frac{18-(-10)}{4}=\frac{18 + 10}{4}=\frac{28}{4}=7$.

Answer:

$7$