JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If the function \(f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} & ,|x| \geq 2 \\ a x^2+2 b, & |x|<2\end{array}\right.\) is differentiable on \(R\), then \(48(a+b)\) is equal to ...........
- A \(15\)
- B \(16\)
- C \(75\)
- D \(78\)
Answer & Solution
Correct Answer
(A) \(15\)
Step-by-step Solution
Detailed explanation
\(f(x)\left\{\begin{array}{c}\frac{1}{\mathrm{x}} ; \mathrm{x} \geq 2 \\ \mathrm{ax}^2+2 \mathrm{~b} ;-2<\mathrm{x}<2 \\ -\frac{1}{\mathrm{x}} ; \mathrm{x} \leq-2\end{array}\right.\) Continuous at \(\mathrm{x}=2 \quad \Rightarrow \frac{1}{2}=\frac{\mathrm{a}}{4}+2 \mathrm{~b}\)…
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