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Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right )> 0$ for all $x \in \left ( 0,1 \right )$. Then $f\left ( x \right )$ has

  1. no local minimum in $(0,1)$
  2. one local maximum in $(0,1)$
  3. exactly one local minimum in $(0,1)$
  4. two distinct local minima in $(0,1)$
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