Question

find the relative rate of change of f(x) at the indicated value of x.
f(x)=405 - 5x; x = 35

the relative rate of change of f(x) at x = 35 is
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Find the derivative of f(x)

The derivative of $f(x)=405 - 5x$ using the power - rule. The derivative of a constant is 0 and the derivative of $-5x$ is $-5$. So, $f^\prime(x)=-5$.

Step2: Calculate f(35)

Substitute $x = 35$ into $f(x)$: $f(35)=405-5\times35=405 - 175=230$.

Step3: Calculate the relative rate of change

The relative rate of change of a function $y = f(x)$ is given by $\frac{f^\prime(x)}{f(x)}$. Substitute $x = 35$, $f^\prime(35)=-5$ and $f(35)=230$ into the formula: $\frac{f^\prime(35)}{f(35)}=\frac{-5}{230}\approx - 0.022$.

Answer:

$-0.022$