After solving it came down to $-(x^{2}+1)$ from the left and $(x^{2}+1)$ from the right, it this correct? and how do i proceed? Any help with this will be highly appreciated.
Continuity and differentiability of $x\left |x\right |+\left ( \frac{\left | x \right |}{x} \right )^3$?
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derivatives
continuity
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1(A), (B), (C) and (D) are meaningless, since it is not known how your function is defined at $x=0$ – 2017-01-26
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0@Fred Actually, all four statements have the same truth value no matter what the function's value at $0$ is. – 2017-01-26
1 Answers
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After solving it came down to $-(x^{2}+1)$ from the left and $(x^{2}+1)$ from the right, it this correct?
Yes, that's correct.
You proceed by looking if the function is continuous (because it can't be differentiable unles it is also continuous).
It should be straightforward to see if the function is continuous at $0$.
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0So it's going to be not continuous? Since, from the left it is -1 and the right it is 1? – 2017-01-26
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0@MAthsjunky Yup. – 2017-01-26