Suppose $f$ is a differentiable function on $[0,1]$, such that the derivative of $f$ is continuous on $[0,1]$. Let $f(1)=6$ and $f(0)=1$. Then $\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{k=1}^n f\left(\frac{k}{n}\right) f^{\prime}\left(\frac{k}{n}\right)$ is

• Correct answer
  A

  $\frac{35}{2}$
• B

  $\frac{25}{2}$
• C

  5
• D

  0

Hence, the correct answer is option: 'A'.