find the relative rate of change of f(x)=120x - 0.2x^2. the relative rate of change of f(x) is □.

Explanation:

Step1: Recall the formula for relative rate of change

The relative rate of change of a function $y = f(x)$ is given by $\frac{f'(x)}{f(x)}$. First, find the derivative of $f(x)=120x - 0.2x^{2}$.

Step2: Differentiate $f(x)$

Using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$, we have $f'(x)=\frac{d}{dx}(120x-0.2x^{2})=120 - 0.4x$.

Step3: Calculate the relative rate of change

The relative rate of change is $\frac{f'(x)}{f(x)}=\frac{120 - 0.4x}{120x-0.2x^{2}}$.

Answer:

$\frac{120 - 0.4x}{120x-0.2x^{2}}$