Problem

Find the general form of $f$ if $f^{\prime}(x)=4 f(x)$.

Answer

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Answer

So, the general form of the function \(f(x)\) is \(\boxed{f(x) = Ce^{4x}}\).

Steps

Step 1 ：The given function is \(f'(x) = 4f(x)\). This is a first order linear differential equation.

Step 2 ：The general solution of this type of differential equation is given by \(f(x) = Ce^{4x}\), where C is a constant.

Step 3 ：So, the general form of the function \(f(x)\) is \(\boxed{f(x) = Ce^{4x}}\).

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