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Let f(x)=a+b|x|+c|x|^4 , where a ,\ b , ...

Let `f(x)=a+b|x|+c|x|^4` , where `a ,\ b ,` and `c` are real constants. Then, `f(x)` is differentiable at `x=0` , if `a=0` (b) `b=0` (c) `c=0` (d) none of these

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`f(x)= a+b|x|+c|x|^4`
`f(0)=a`
(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+b|0-h|+c|0-h|^4-a)/(0-h-0) `
` =lim_(h->0)(-b-ch^3) `
(RHD at x=0)=`lim_(x->0^+)(f(x)-f(0))/(x-0)`
`=lim_(h->0)(f(0+h)-f(0))/(0+h-0)`
...
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