AP EAMCET · Maths · Continuity and Differentiability
If \(f(x)=\left\{\begin{array}{cc}2 x+3, & x \leq 1 \\ a x^2+b x, & x\gt1\end{array}\right.\) is differentiable \(\forall x \in \mathbb{R}\), then \(f(2)=\)
- A 5
- B 4
- C -4
- D -10
Answer & Solution
Correct Answer
(C) -4
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cc}2 x+3, & x \leq 1 \\ a x^2+b x & , x\gt1\end{array}\right.\) \(f(x)\) is differentiable \(\forall x \in \mathbf{R}\) \(\Rightarrow \lim _{x \rightarrow 1^{-}} f^{\prime}(x)=\lim _{x \rightarrow 1^{+}} f^{\prime}(x) \Rightarrow 2=2 a+b\)…
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