Let $f:(0,3) \cup(6,9) \rightarrow \mathbb{R}$ be a differentiable function such that $f^{\prime}(x)=\frac{1}{2}$ for all $x \in(0,3) \cup(6,9)$. Then

• A

  $f$ is an increasing function.
• B

  $f$ is a one to one function.
• Correct answer
  C

  $f(8)-f(7)=f(2)-f(1)$.
• Correct answer
  D

  there exists a number $c$ in $\mathbb{R}$ such that $f(x+6)=f(x)+c$ for all $x \in(0,3)$.

Hence, the correct answer is options: 'C', 'D'.