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Discuss the differentiability of f(x)...

Discuss the differentiability of `f(x)=x|x|` at `x=0` .

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Verified by Experts

Given that,
`f(x)=x|x|`
`={{:(x^2; if xge0),(-x^2; if x<0):}`
`f'(x)={{:(2x;if x≥0),(−2x;if x<0):}`
`LHD` of `f(x)` at `(x=0^-)`
`=-2(0)`
`=0`
`RHD` of `f(x)` at `(x=0^+)`
`=2(0)`
`=0`
`LHD=RHD`
`f(x)=x∣x∣` is differentiable at `x=0`. ​
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