Question

find the relative rate of change of f(x) at the indicated value of x. f(x)=246 - 3x, x = 20 the relative rate of change of f(x) at x = 20 is □. (type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Recall the formula for relative - rate of change

The relative rate of change of a function $y = f(x)$ is given by $\frac{f^{\prime}(x)}{f(x)}$. First, find the derivative of $f(x)=246 - 3x$. Using the power - rule, if $y = ax + b$, then $y^{\prime}=a$. So, $f^{\prime}(x)=-3$.

Step2: Evaluate $f(x)$ and $f^{\prime}(x)$ at $x = 20$

When $x = 20$, $f(20)=246-3\times20=246 - 60 = 186$. And $f^{\prime}(20)=-3$.

Step3: Calculate the relative rate of change

The relative rate of change of $f(x)$ at $x = 20$ is $\frac{f^{\prime}(20)}{f(20)}=\frac{-3}{186}=-\frac{1}{62}\approx - 0.016$.

Answer:

$-0.016$