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Let $f$ be a twice differentiable function defined on R such that $f (0) = 1, f^{'} (0) = 2$ and $f^{1} (x) \neq 0$ for all $x \in R$ . If $|\begin{matrix} f (x) & f^{'} (x) \\ f^{'} (x) & f^{"} (x) \end{matrix}| = 0$ for all $x \in R$ , then the value of $f (1)$ lies in the interval

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Correct option is A

fxf"x=f1x2⇒ f1x2−fxf11xf1x2=0 ⇒ ddxfxf1x=0⇒ fxf1x=k ⇒ k=12fx=±ke2x f0=1⇒f1=e2=7.38

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Let f be a twice differentiable function defined on R such that f0=1,f'0=2and f1x≠0for all x∈R . If fxf'xf'xf"x=0 for all x∈R, then the value of f1 lies in the interval

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Let $f$ be a twice differentiable function defined on R such that $f (0) = 1, f^{'} (0) = 2$ and $f^{1} (x) \neq 0$ for all $x \in R$ . If $|\begin{matrix} f (x) & f^{'} (x) \\ f^{'} (x) & f^{"} (x) \end{matrix}| = 0$ for all $x \in R$ , then the value of $f (1)$ lies in the interval