find the average rate of change of g(x)=2x^2 - 4x from x = 2 to x = 7. 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, $a = 2$, $b = 7$, and $g(x)=2x^{2}-4x$.

Step2: Calculate $g(7)$

Substitute $x = 7$ into $g(x)$: $g(7)=2\times7^{2}-4\times7=2\times49 - 28=98 - 28=70$.

Step3: Calculate $g(2)$

Substitute $x = 2$ into $g(x)$: $g(2)=2\times2^{2}-4\times2=2\times4-8 = 8 - 8=0$.

Step4: Calculate the average rate of change

Using the formula $\frac{g(b)-g(a)}{b - a}$, we have $\frac{g(7)-g(2)}{7 - 2}=\frac{70 - 0}{5}=\frac{70}{5}=14$.

Answer:

$14$