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Let f:R⃗->R be a function defined by f(x...

Let `f:R⃗->R` be a function defined by `f(x)=Min{x+1,|x|+1}` . Then which of the following is true? (1) `f(x) >= 1` for all `x in R` (2) `f(x)` is not differentiable at `x=1` (3) `f(x)` is differentiable everywhere (4) `f(x)` is not differentiable at `x=0`

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Knowledge Check

  • Let f:R to R be a function defined by f(x) = min {x+1,|x|+1} . Then which of the following is true.

    A
    `f(x)ge 1` for `x in R`
    B
    f(x) is not differentiable at x = 1
    C
    f(x) is differentiable everywhere
    D
    f(x) is not differentiable at x = 0

  • Let f: R to R be a function defined by f(x)="min" {x+1,|x|+1}. Then, which of the following is true?

    A
    `f(x) gt 1"for all " x in R`
    B
    `f(x)"is not differentiable at x=1"`
    C
    `f(x)"is everywhere differentiable"`
    D
    `f(x)"is not differentiable at x=0"`

  • Let f: R to R be a function defined by f (x) = max { x, x^3 } . The set of all points where f (x) in not differentiable is:

    A
    `{-1,1}`
    B
    `{-1,0}`
    C
    {0,1}
    D
    `{-1,0,1}`

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