Question

Preview of Differential Equations:

Given each of the following equations involving a functionf, find a possible formula for f(x).

$f\text{'}\left(x\right)=2f\left(x\right)$

Short answer

The possible formula for the function $f\text{'}\left(x\right)=2f\left(x\right)$is $f\left(x\right)=e^{2x}$.

Step-by-step solution

Step 1. Given Information.

The function:

$f\text{'}\left(x\right)=2f\left(x\right)$

Step 2. Consider the function.

Consider the function,

$$\begin{gathered} f\left(x\right)=e^{2x} \\ f\text{'}\left(x\right)=\frac{d}{dx}{e}^{2x} \\ =2e^{2x} \\ =2f\left(x\right) \end{gathered}$$

So the function is $f\left(x\right)=e^{2x}$.