Question

find the average rate of change of (k(x)= - 2x^{2}) over the interval (-6,-4). write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = k(x)$ over the interval $[a,b]$ is $\frac{k(b)-k(a)}{b - a}$. Here, $a=-6$, $b = - 4$, and $k(x)=-2x$.

Step2: Calculate $k(a)$ and $k(b)$

First, find $k(-6)$: $k(-6)=-2\times(-6)=12$. Then, find $k(-4)$: $k(-4)=-2\times(-4)=8$.

Step3: Substitute into the formula

Substitute $k(-6) = 12$, $k(-4)=8$, $a=-6$, and $b = - 4$ into the average - rate - of - change formula $\frac{k(b)-k(a)}{b - a}$. We get $\frac{8 - 12}{-4-(-6)}=\frac{8 - 12}{-4 + 6}=\frac{-4}{2}=-2$.

Answer:

$-2$