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If f(x)=|3-x|+(3+x), where (x) denotes t...

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`
continuous but not differentiable at `x=3`
differentiable but not continuous at `x=3`
neither differentiable nor continuous at `x=3`

Text Solution

Verified by Experts

Given
`f(x)=|3-x|+3+x`
`f(x)={3-x+x+3,2 < x < 3` and `x-3+x+4,3 < x < 4}`
Or,`f(x)={9-x,2 < x < 3` and `x+4,3 < x < 4}`
Checking continuity at `x=3`
Here,`L.H.L`at `x=3`
`lim_(x->3^(-))(9-x)=6`
R.H.L at `x=3`
...
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