If f(x)=||x-1|+|x-3|-|2x-1||+||x-1|+|x-3...

If `f(x)=||x-1|+|x-3|-|2x-1||+||x-1|+|x-3|+|2x-1||`, then

A

`f(x)` is non-differentiable at `x=1`

B

`f(x)` is non differentiable at `x=3/2`

C

`f(x)` has minimum value is 2

D

`x=1` is point of local minima

Verified by Experts

The correct Answer is:

A, B, C

`:'f(x)=2xx"max"{|x-1|+|x-3|,|2x-1|}`
`:.x=1, 3/2` point of non-differentiability and minimum value is 2

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