find the average rate of change of f(x)= - 7x+2 from 2 to 6. the average rate of change of f(x)= - 7x+2 from…

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 6$, and $f(x)=-7x + 2$.

Step2: Calculate $f(6)$

Substitute $x = 6$ into $f(x)$: $f(6)=-7\times6 + 2=-42 + 2=-40$.

Step3: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$: $f(2)=-7\times2+2=-14 + 2=-12$.

Step4: Calculate the average rate of change

$\frac{f(6)-f(2)}{6 - 2}=\frac{-40-(-12)}{4}=\frac{-40 + 12}{4}=\frac{-28}{4}=-7$.

Answer:

$-7$