given the function g(x)=-x² + 5x + 14, determine the average rate of change of the function over the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a = 1$, $b = 9$, and $g(x)=-x^{2}+5x + 14$.

Step2: Calculate $g(9)$

Substitute $x = 9$ into $g(x)$: $g(9)=-(9)^{2}+5\times9 + 14=-81 + 45+14=-22$.

Step3: Calculate $g(1)$

Substitute $x = 1$ into $g(x)$: $g(1)=-(1)^{2}+5\times1 + 14=-1 + 5+14=18$.

Step4: Calculate the average rate of change

$\frac{g(9)-g(1)}{9 - 1}=\frac{-22-18}{8}=\frac{-40}{8}=-5$.

Answer:

$-5$