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The function {:(f (x) =ax (x-1)+b, x lt ...

The function `{:(f (x) =ax (x-1)+b, x lt 1),( =x-1, 1 le x le 3),( =px ^(2)+qx +2, x gt 3):}`
if (i) f (x) is continous for all x
(ii) ` f'(1)` does not exist
(iii) `f '(x)` is continous at `x=3,` then

Answer

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Knowledge Check

  • f(x) = {{:(-1, x lt -1),(-x, -1 le x le 1),(1, x gt 1):} is continous

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    B
    at x=-1 but not at x=1
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  • If f(x) =ax^(2) +b, b ne 0, x le 1 =bx^(2) +ax + c, x gt 1 , then f(x) is continous and differentiable at x=1, if

    A
    c=0, a=2b
    B
    a=b, c= arbitrary
    C
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  • If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

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