If $2 f(x)=f^{\prime}(x)$ and $f(0)=3$, then $f(2)$ is equal to
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If $2 f(x)=f^{\prime}(x)$ and $f(0)=3$, then $f(2)$ is equal to

(A) $3 e^4$

(B) $3 e^2$

(C) $e^4$

(D) None of these

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Best answer

SOLUTION —

Let, $f(x)=3 e^{2 x}$

$\Rightarrow \quad f^{\prime}(x)=6 e^{2 x}=2 f(x)$

$\therefore$ Our assumption is true.

$\therefore \quad f(2)=3 e^{2 \times 2}=3 e^4$

So, The correct option will be (A).

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