Q3 of 64 Page 10

Choose the correct answer.

The set of points where the function f(x) = x|x| is differentiable is


We have f(x) = x|x|


Where


We have –x2 and x2 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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