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Limits Continuity and Differentiability question

2021 · 18 Mar · Shift 1 · Q36

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 18 Mar · Shift 1 · Q36

Limits Continuity and Differentiability question

2021 · 18 Mar · Shift 1 · Q36

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If

f(x) = \left\{ {\begin{matrix} {{1 \over {|x|}}} & {;\,|x|\, \ge 1} \\ {a{x^2} + b} & {;\,|x|\, \lt 1} \\ \end{matrix} } \right.

is differentiable at every point of the domain, then the values of a and b are respectively :

A
${1 \over 2},{1 \over 2}$
B
${1 \over 2}, - {3 \over 2}$
C
${5 \over 2}, - {3 \over 2}$
D
$- {1 \over 2},{3 \over 2}$

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