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JEE Math Practice Question

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

  1. A.(0, 3)
  2. B.(9, 12)
  3. C.(3, 6)
  4. D.(6, 9)

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