Question

question 2
find the average rate of change of the function $f(x)=x^{2}-x - 7$, over the interval $2,5$.
average rate of change =

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, $a = 2$, $b = 5$, and $f(x)=x^{2}-x - 7$.

Step2: Calculate $f(5)$

Substitute $x = 5$ into $f(x)$:
$f(5)=5^{2}-5 - 7=25-5 - 7=13$.

Step3: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$:
$f(2)=2^{2}-2 - 7=4-2 - 7=-5$.

Step4: Calculate the average rate of change

$\frac{f(5)-f(2)}{5 - 2}=\frac{13-(-5)}{3}=\frac{13 + 5}{3}=\frac{18}{3}=6$.

Answer:

$6$