Question

given f(x)=17 - x^2, what is the average rate of change in f(x) over the interval 1, 5?
-6
-\frac{1}{2}
\frac{1}{4}
1

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 5$, and $f(x)=17 - x^{2}$.

Step2: Calculate $f(1)$

Substitute $x = 1$ into $f(x)$: $f(1)=17-1^{2}=17 - 1=16$.

Step3: Calculate $f(5)$

Substitute $x = 5$ into $f(x)$: $f(5)=17-5^{2}=17 - 25=-8$.

Step4: Calculate the average rate of change

$\frac{f(5)-f(1)}{5 - 1}=\frac{-8 - 16}{4}=\frac{-24}{4}=-6$.

Answer:

-6