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The minimum value of $f(x)=\ln \left(1+\exp \left(x^{2}-3 x+2\right)\right)$ for $x \geq 0$, where $\ln (\cdot)$ denotes the natural logarithm, is

  1. $\ln \left(1+e^{-1 / 4}\right)$
  2. $\ln (5 / 3)$
  3. $0$ 
  4. $\ln \left(1+e^{2}\right)$
  5. None of the above

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