WBJEE · Maths · Continuity and Differentiability
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
- A \(a=3, b=5\)
- B \(a=0, b=5\)
- C \(a=0, b=3\)
- D \(a=b=3\)
Answer & Solution
Correct Answer
(A) \(a=3, b=5\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{LHL}=\mathrm{RHL} \Rightarrow 4+\mathrm{a}=\mathrm{b}+2 \\ & \mathrm{LHD}=\mathrm{RHD} \Rightarrow \mathrm{b}=5 \Rightarrow \mathrm{a}=3\end{aligned}\)
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