find the average rate of change of $f(x)=2x^{2}-7x$ from $x = 2$ to $x = 5$. 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, $a = 2$, $b = 5$, 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 $f(5)$

Substitute $x = 5$ into $f(x)$: $f(5)=2\times5^{2}-7\times5=2\times25-35 = 50 - 35 = 15$.

Step4: Calculate the average rate of change

$\frac{f(5)-f(2)}{5 - 2}=\frac{15-(-6)}{3}=\frac{15 + 6}{3}=\frac{21}{3}=7$.

Answer:

7