Question

find the percentage rate of change of f(x) at the indicated value of x. f(x)=130 + 34x; x = 6. the percentage rate of change of f(x) at x = 6 is %. (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Find the derivative of f(x)

The derivative of $f(x)=130 + 34x$ is $f'(x)=34$ (since the derivative of a constant 130 is 0 and the derivative of $34x$ using the power - rule is 34).

Step2: Evaluate f(x) at x = 6

$f(6)=130+34\times6=130 + 204=334$.

Step3: Calculate the percentage rate of change

The percentage rate of change of $y = f(x)$ is given by $\frac{f'(x)}{f(x)}\times100\%$. Substitute $x = 6$, $f'(6)=34$ and $f(6)=334$ into the formula: $\frac{34}{334}\times100\%=\frac{3400}{334}\% \approx 10.2\%$.

Answer:

$10.2$