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Limits Continuity and Differentiability question

2020 · 4 Sep · Shift 2 · Q40

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JEE Main
Mathematics
Limits Continuity and Differentiability
2020 · 4 Sep · Shift 2 · Q40

Limits Continuity and Differentiability question

2020 · 4 Sep · Shift 2 · Q40

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

The function

f(x) = \left\{ {\begin{matrix} {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} \\ {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| \gt 1} \\ \end{matrix} } \right.

is :

A
continuous on R–{–1} and differentiable on R–{–1, 1}
B
both continuous and differentiable on R–{1}
C
both continuous and differentiable on R–{–1}
D
continuous on R–{1} and differentiable on R–{–1, 1}

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