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Let f (x) = {{:( x ^(2) - 3x + 2 "," , x...

Let `f (x) = {{:( x ^(2) - 3x + 2 "," , x lt 2 ), ( x ^(3) - 6x ^(2) + 9x + 2 "," , xge 2 ):}`
Then

A

`lim _( x to 2) f (x) ` does not exist

B

f is continuous at `x =2`

C

f is continuous but not differentiable at `x =2`

D

f is continuous and differentiable at `x =2`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • Let f(x)={{:(x^(3)-1",", x lt2),(x^(2)+3"," , x ge 2):} Then

    A
    `f^(-1)(x)={{:((x+1)^(1//3)",", x lt2),((x-3)^(1//2)+"," , x ge 2):}`
    B
    `f^(-1)(x)={{:((x+1)^(1//3)",", x lt 7),((x-3)^(1//2)+"," , x ge 7):}`
    C
    `f^(-1)(x)={{:((x+1)^(1//3)",", x lt 1),((x-3)^(1//2)+"," , x ge 7):}`
    D
    `f^(-1)(x)` does not exist

  • Let f (x) = {{:( x "," , x lt 1), ( 2-x |"," , 1 lt x le 2 "then" f (x) is), ( -2 + 3x -x ^(2)",", x gt 2 ):}

    A
    differentiable at `x =1`
    B
    differentiable at `x =2`
    C
    differentiable at `x=1 and x =2`
    D
    None of these

  • If f(x) - 3x^(2) + 6x -9 , then

    A
    `f(x)` is increasing in `(-1, 3)`
    B
    `f(x)` is decreasing in `(3, infty)`
    C
    `f(x)` is increasing in `(-infty, -1)`
    D
    `f(x)` is decreasing in `(-infty, -1)`

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