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JEE Main 30-Jan-2024 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 30-Jan-2024 Paper - Shift 14 Marks
Question
If the function $f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} & ,|x| \geq 2 \\ ax ^2+2 b, & |x|<2\end{array}\right.$ is differentiable on R, then 48 (a + b) is equal to ________.
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Answer

(15)
$f(x)\left\{\begin{array}{c}\frac{1}{x} ; x \geq 2 \\ ax ^2+2 b ;-2 < x < 2 \\ -\frac{1}{x} ; x \leq-2\end{array}\right.$
Continuous at $x=-2 \quad \Rightarrow \frac{1}{2}=\frac{a}{4}+2 b$
Since, it is differentiable at $x =2$
$-\frac{1}{x^2}=2 ax$
Differentiable at $x =2 \quad \Rightarrow \frac{-1}{4}=4 a \Rightarrow a =\frac{-1}{16}, b$
$=\frac{3}{8}$

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