find the average rate of change of $g(x)=2x^{2}-7x$ from $x = 1$ 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 $y = g(x)$ from $x = a$ to $x = b$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a = 1$, $b = 5$, and $g(x)=2x^{2}-7x$.

Step2: Calculate $g(5)$

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

Step3: Calculate $g(1)$

Substitute $x = 1$ into $g(x)$: $g(1)=2\times1^{2}-7\times1=2 - 7=-5$.

Step4: Calculate the average rate of change

$\frac{g(5)-g(1)}{5 - 1}=\frac{15-(-5)}{4}=\frac{15 + 5}{4}=\frac{20}{4}=5$.

Answer:

$5$