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Let f (x)= {{:(ac (x-1)+b,,, x lt 1),( x...

Let `f (x)= {{:(ac (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +qx +2,,, x gt 3):}` is continous `AA x in R` except `x =1` but `|f (x)|` is differentiable everywhere and `f '(x)` is continous at `x=3 and |a+p+q|=k,` then k=

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Let f(x)={ax(x-1)+b;x 3 is contnuous AA x in R except x-1 and |f(x)| is differentiable every where and f'(x) is continuous at x=3.

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

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

    A
    at x=1 but not at x=-1
    B
    at x=-1 but not at x=1
    C
    at both x=1 and x=-1
    D
    at none of x=1 and -1

  • If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

    A
    It has a relative minimum at x = 1
    B
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    C
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    D
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  • Let f (x) = {{:( x ^(2) -1 ",", x le 1),(k (x-1) "," , x gt 1):} then :

    A
    f is continuous for only finitely many vlaues of k
    B
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    D
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