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Let f(x)={{:(3^x","-1lexle1),(4-x","1ltx...

Let `f(x)={{:(3^x","-1lexle1),(4-x","1ltxle4):}` then

A

`f(x)` is continuous and derivable at `x=1`

B

`f(x)` is discontinuous and non-derivable at `x=1`

C

`f(x)` is continuous and non-derivable at `x=1` because `f'(1)` and `f'(1)=3 l n3`

D

`f(x)` is continuous and non-derivable at `x=1` because `f'(1^(+))=-1` and `f'(1^(-))=1`

Text Solution

Verified by Experts

The correct Answer is:
C
`becausef(x)=3=f(1^(-))` and `f(1^(+))=3`
`therefore` continuous at `x=1`
`becausef'(x)={{:(3^(x)l n 3,-1lexlt1),(-1,1ltxle4):}`
`thereforef'(1^(+))=-1`
`therefore f'(1^(-))=3 l n3`
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