Question

1. calculator - active. find the average rate of change of the function (w(r)=sqrt{1 - 4r}) on the interval (-5leq rleq - 1).

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $y = w(r)$ on the interval $[a,b]$ is $\frac{w(b)-w(a)}{b - a}$. Here, $a=-5$, $b = - 1$, and $w(r)=\sqrt{1 - 4r}$.

Step2: Calculate $w(-1)$

Substitute $r=-1$ into $w(r)$: $w(-1)=\sqrt{1-4\times(-1)}=\sqrt{1 + 4}=\sqrt{5}$.

Step3: Calculate $w(-5)$

Substitute $r = - 5$ into $w(r)$: $w(-5)=\sqrt{1-4\times(-5)}=\sqrt{1 + 20}=\sqrt{21}$.

Step4: Calculate the average rate of change

$\frac{w(-1)-w(-5)}{-1-(-5)}=\frac{\sqrt{5}-\sqrt{21}}{-1 + 5}=\frac{\sqrt{5}-\sqrt{21}}{4}$.

Answer:

$\frac{\sqrt{5}-\sqrt{21}}{4}$