Question

find the average rate of change of $g(x)=2x^{2}+7$ from $x = 5$ to $x = 9$. simplify your answer as much as possible.

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, $a = 5$, $b = 9$, and $g(x)=2x^{2}+7$.

Step2: Calculate $g(9)$

Substitute $x = 9$ into $g(x)$: $g(9)=2\times9^{2}+7=2\times81 + 7=162+7=169$.

Step3: Calculate $g(5)$

Substitute $x = 5$ into $g(x)$: $g(5)=2\times5^{2}+7=2\times25 + 7=50 + 7=57$.

Step4: Calculate the average rate of change

Substitute $g(9)$ and $g(5)$ into the average - rate - of - change formula: $\frac{g(9)-g(5)}{9 - 5}=\frac{169 - 57}{4}=\frac{112}{4}=28$.

Answer:

28