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Let $f(x)=(x-1)(x-2)(x-3)g(x); \: x\in \mathbb{R}$ where $g$ is twice differentiable function. Then

  1. there exists $y\in(1,3)$ such that $f’’(y)=0.$
  2. there exists $y\in(1,2)$ such that $f’’(y)=0.$
  3. there exists $y\in(2,3)$ such that $f’’(y)=0.$
  4. none of the above is true.
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