let $f(x)=log x$. what is the average rate of change of $f(x)$ from 4 to 6? round to the nearest hundredth…

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, $a = 4$, $b = 6$, and $f(x)=\log x$.

Step2: Calculate $f(6)$ and $f(4)$

$f(6)=\log 6$ and $f(4)=\log 4$.

Step3: Substitute into the formula

The average rate of change is $\frac{\log 6-\log 4}{6 - 4}=\frac{\log\frac{6}{4}}{2}=\frac{\log\frac{3}{2}}{2}$. Since $\log\frac{3}{2}\approx\log1.5\approx0.1761$, then $\frac{\log1.5}{2}\approx\frac{0.1761}{2}=0.08805\approx0.09$.

Answer:

A. 0.09