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The set of points where the function f(x...

The set of points where the function `f(x)=x|x|` is differentiable is `(-oo,oo)` (b) `(-oo,0)uu(0,oo)` `(0,oo)` (d) `[0,oo)`

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We have,` f(x)={x^2,x>=0 and −x^2,​x<0​}`
Clearly, f(x) is differentiable for all x>0 and for all x<0
So, we check the differentiability at x=0.
`R.H.D` at x=a
=`(d/dx)​(x^2)_(x=0)​=(2x)_(x=0)​=0 `
...
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