Choose the correct answer. The set of points where the function f(x) = x|x| is differentiable is

Question

Philoid · Accepted Answer

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 (–∞, ∞).