If f(x)=a|sinx|+b\ e^(|x|)+c\ |x|^3 and ...

If `f(x)=a|sinx|+b\ e^(|x|)+c\ |x|^3` and if `f(x)` is differentiable at `x=0` , then `a=b=c=0` (b) `a=0,\ \ b=0;\ \ c in R` (c) `b=c=0,\ \ a in R` (d) `c=0,\ \ a=0,\ \ b in R`

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Given that,
`f(x)=a|sinx|+b\ e^(|x|)+c\ |x|^3`
`f(0)=b`
LHD at `x=0`=`(lim)_(x->0^-)(f(x)-f(0))/(x-0)`
`= (lim)_(h->0)(f(0-h)-f(0))/(0-h-0)`
`= (lim)_(h->0) ( a|sin(-h)|+b\ e^(|-h|)+c|-h|^3-b)/(-h)`
`=-a`
RHD at `x=0`=`(lim)_(x->0^+)(f(x)-f(0))/(x-0)`
...

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