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Let $I=(a, b)$ be an open interval and let $f$ be a function which is differentiable on $I$. Which of the followings is/are true statements -

  1. If $f^{\prime}(x)=0$ for all $x \in I$, then there is a constant $r$ such that $f(x)=r$ for all $x \in I$.
  2. If $f^{\prime}(x)>0$ for all $x \in I$, then $f(x)$ is strictly increasing on $I$.
  3. If $f^{\prime}(x)<0$ for all $x \in I$, then $f(x)$ is strictly decreasing on $I$.
  4. If $f^{\prime}(x)>0$ for all $x \in I$, then $f(x)$ is strictly decreasing on $I$.
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