Answer :

We have f(x) = x|x|

Where

We have –x^{2} and x^{2} which being polynomial functions are continuous and differentiable.

The only possible point of non-differentiability can be x =0.

LHD at x =0,

RHD at x =0,

∵ LHD = RHD = f(0)

∴ f(x) is differentiable at x =0.

Hence f(x) is differentiable at (–∞, ∞).

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