Q83 / 155 · WBJEE 2025 · Mathematics

If $f(x)=\left\{\begin{array}{ll}x^2+3 x+a, & x \leq 1 \\ b x+2, & x\gt1\end{array}, x \in \mathbb{R}\right.$, is everywhere differentiable, then

  • Correct answer
    A
    $a=3, b=5$
  • B
    $a=0, b=5$
  • C
    $a=0, b=3$
  • D
    $a=b=3$

Solution

$\begin{aligned} & \mathrm{LHL}=\mathrm{RHL} \Rightarrow 4+\mathrm{a}=\mathrm{b}+2 \\ & \mathrm{LHD}=\mathrm{RHD} \Rightarrow \mathrm{b}=5 \Rightarrow \mathrm{a}=3\end{aligned}$

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

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