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Let f(x) = x|x|. The set of points, whe...

Let ` f(x) = x|x|`. The set of points, where f (x) is twice differentiable, is ….. .

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The correct Answer is:
`x in R - {0}`
Given, `f(x) = x|x|`
` rArr" "f(x) ={{:(x^(2)" if" x ge0),(-x^(2)", if" xlt0):}`
f(x) is not differentiable at x = 0 but all R -{0}.
Therefore, `f'(x) ={{:(2x", " x gt 0),(-2x", " x lt 0):}`
` rArr" " f''(x) ={{:(2", " x gt 0),(-2", " x lt0):}`
Therefore, f(x) is twice differentiable for all ` x in R -{0}`.
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