Suppose \( \left|\begin{array}{ll}f^{\prime}(x) & f(x) \\ f^{\prime...

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Suppose \( \left|\begin{array}{ll}f^{\prime}(x) & f(x) \\ f^{\prime \prime}(x) & f^{\prime}(x)\end{array}\right|=0 \) where \( f(x) \) is
\( \mathrm{P} \)
W
continuously differentiable function \( f^{\prime}(x) \neq 0 \) and satisfies \( f(0)=1 \) and \( f^{\prime}(0)=2 \) then \( f(x) \) is:
(1) \( x^{2}+2 x+1 \)
(2) \( 2 e^{x}-1 \)
(3) \( e^{2 x} \)
(4) \( 4 e^{x / 2}-3 \)
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