Let $a, b \in \mathbb{R}$ and $f$ be the function defined by
$f(x)= \begin{cases}e^x, & \text { if } x \lt 5 \\ a+b x, & \text { if } x \geq 5\end{cases}$
If $f$ is differentiable and $f^{\prime}$ is continuous on $\mathbb{R}$, then

• Correct answer
  A

  $a+4 b=0$
• B

  $a-4 b=0$
• C

  $a-6 b=0$
• D

  $a+6 b=0$

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