Find the relative rate of change of $f (x) = 21 + 3 e^{- 3 x}$ .
The relative rate of change of $f (x)$ is

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Answer

Final Answer: The relative rate of change of $f (x) = 21 + 3 e^{- 3 x}$ is $- \frac{9 e^{- 3 x}}{21 + 3 e^{- 3 x}}$ .

Steps

Step 1 ：Given the function $f (x) = 21 + 3 e^{- 3 x}$ , we are asked to find the relative rate of change.

Step 2 ：The relative rate of change of a function $f (x)$ is given by the derivative of the function divided by the function itself.

Step 3 ：First, we find the derivative of $f (x)$ , which is $- 9 e^{- 3 x}$ .

Step 4 ：Then, we divide this derivative by the original function to get the relative rate of change: $- \frac{9 e^{- 3 x}}{21 + 3 e^{- 3 x}}$ .

Step 5 ：Final Answer: The relative rate of change of $f (x) = 21 + 3 e^{- 3 x}$ is $- \frac{9 e^{- 3 x}}{21 + 3 e^{- 3 x}}$ .