find the average rate of change of g(x)=3x² - 8x from x = 1 to x = 6. simplify your answer as much as…

Answer:

$13$

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, $a = 1$, $b = 6$, and $g(x)=3x^{2}-8x$.

Step2: Calculate $g(6)$

Substitute $x = 6$ into $g(x)$: $g(6)=3\times6^{2}-8\times6=3\times36 - 48=108 - 48 = 60$.

Step3: Calculate $g(1)$

Substitute $x = 1$ into $g(x)$: $g(1)=3\times1^{2}-8\times1=3 - 8=-5$.

Step4: Calculate the average rate of change

$\frac{g(6)-g(1)}{6 - 1}=\frac{60-(-5)}{5}=\frac{60 + 5}{5}=\frac{65}{5}=13$.