Question

find the average rate of change of k(x) = -2x² 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 the 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 $k(x)=-2x^{2}$.

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

First, find $k(-6)$:
$k(-6)=-2\times(-6)^{2}=-2\times36=-72$.
Then, find $k(-4)$:
$k(-4)=-2\times(-4)^{2}=-2\times16=-32$.

Step3: Substitute into the formula

$\frac{k(-4)-k(-6)}{-4-(-6)}=\frac{-32 - (-72)}{-4 + 6}=\frac{-32 + 72}{2}=\frac{40}{2}=20$.

Answer:

20