Respuesta :

W0lf93
One nonzero function that satisfies f′(x)=4f(x) can be found by using the constant 'e' and its derivative rules. If we define f(x) = e^(4x), the first derivative f'(x) can be found via the chain rule to be 4*e^(4x) or the 4*f(x) as desired.
facundo3141592

We want to solve in a general way the given differential equation.

The function we want to get is:

[tex]f(x) = A*e^{4*x}[/tex]

Let's see how to get that function.

we have:

[tex]f'(x) = 4*f(x)[/tex]

From this we can assume that the function f(x) is an exponential function of the form:

[tex]f(x) = A*e^{4*x}[/tex]

So when we differentiate it, the only thing that happens is that the 4 comes down as a factor:

[tex]\frac{df}{dx} = 4*A*e^{4x} = 4*f(x)[/tex]

This is the nonzero function that we wanted, where A can be any real number different than zero.

If you want to learn more, you can read:

https://brainly.com/question/14620493

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