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Limits Continuity and Differentiability question

2008 · Shift 0 · Q31

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PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2008 · Shift 0 · Q31

Limits Continuity and Differentiability question

2008 · Shift 0 · Q31

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f\left( x \right) = \left\{ {\begin{matrix} {\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x e 1} \\ 0 & {if\,x = 1} \\ \end{matrix} } \right.

Then which one of the following is true?

A
$f$ is neither differentiable at x = 0 nor at x = 1
B
$f$ is differentiable at x = 0 and at x = 1
C
$f$ is differentiable at x = 0 but not at x = 1
D
$f$ is differentiable at x = 1 but not at x = 0

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