If `f(x)=|3-x|+(3+x)` , where `(x)` denotes the least integer greater than or equal to `x` , then `f(x)` is continuous and differentiable at `x=3` (b) continuous but not differentiable at `x=3` (c) differentiable but not continuous at `x=3` (d) neither differentiable nor continuous at `x=3`

Explanation

`f(x)= |3-x|+(3+x)`

(L.H.L at x=3)=` lim_(x->3^-)f(x)`

`= lim_(h->0)f(3-h)`

`=lim_(h->0) |3-3+h|+(3+3-h)`

`=lim_(h->0) |h|+(6+h)`

`=6`

(R.H.L at x=3)=` lim_(x->3^+)f(x)`

`= lim_(h->0)f(3+h)`

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