Let $$f\left( x \right) = \left\{ {\matrix{ {\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x \ne 1} \cr 0 & {if\,x = 1} \cr } } \right.$$ Then which one of the following is true?

Question

Let $$f\left( x \right) = \left\{ {\matrix{ {\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x \ne 1} \cr 0 & {if\,x = 1} \cr } } \right.$$

Then which one of the following is true?

$f$ is neither differentiable at x = 0 nor at x = 1

$f$ is differentiable at x = 0 and at x = 1

$f$ is differentiable at x = 0 but not at x = 1

$f$ is differentiable at x = 1 but not at x = 0

Solution

Please login to view the detailed solution steps...

Go to DASH