Differentiability of Piecewise Function... |JEE Main 2021| CD

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JEE MAIN 2021

18-03-21 S1

Question

If $\quad f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} ; & |x| \geq 1 \\ a x^2+b ; & |x|<1\end{array}\right.$ is differentiable at every point of the domain, then the values of $a$ and $b$ are respectively :

Select the correct option:

A

$\frac{1}{2}, \frac{1}{2}$

B

$\frac{1}{2},-\frac{3}{2}$

C

$\frac{5}{2},-\frac{3}{2}$

D

$-\frac{1}{2}, \frac{3}{2}$

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