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GATE BT 2025 | Question: 36

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​​​​If the function
$$ f(x)=\left\{\begin{array}{ll}
\sin 2 x, & \text { for } x>0 \\
a+b x, & \text { for } x \leq 0
\end{array}\right.$$

where $a$ and $b$ are constants, is differentiable at $x=0$, then $a+b$ is equal to

  1. $0$
  2. $1$
  3. $2$
  4. $3$

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